Žigić was born in Bačka Topola, in what was then SFR Yugoslavia, the son of Jovan, a former footballer, and his wife Milica, who had been a basketball player. He completed his secondary education at the mechanical engineering school in Bačka Topola. His brother Branko, 15 months his junior, also became a footballer, as a central defender with clubs including Cement Beočin and Serbian First League club Proleter Novi Sad. During the Yugoslav Wars in 1999, Žigić’s hometown was beneath the flight-path of NATO bombers heading for Belgrade; for much of that part of the conflict, the family home was without electricity or running water.

Žigić signed his first professional contract in January 2003, with Red Star Belgrade, one of the biggest clubs in the country. Because he was not considered ready for first-team football at that level, he spent the latter part of the 2002–03 season on loan at Spartak Subotica, another third-tier side, for whom his goalscoring rate was even higher: 14 goals from just 11 league games.

Coach Ilija Petković gave Žigić his international debut for Serbia and Montenegro on 31 March 2004, as an 84th-minute substitute in a 1–0 friendly defeat against Norway in Belgrade. His next appearance and first start came some 14 months later; in a friendly against Italy in Canada, he ran onto a through ball and went round the goalkeeper to open the scoring and also hit the post in a 1–1 draw.

In September 2005, Žigić signed a one-year extension to his contract, which had been due to expire at the end of the season. He helped his team progress through the qualifying rounds of the UEFA Cup, and according to Reuters’ correspondent, “capped a brilliant individual performance with two goals” as well as providing the cross for Milan Purović as Red Star beat Roma 3–1 in the third match of the group stage. His first goal, a header, appeared to have been scored from an offside position, but for the second, in the 86th minute, he dispossessed Philippe Mexès, evaded two more opponents, and bent the ball into the top corner from 25 m (27 yd) with his weaker left foot. He said afterwards, “I’ve never scored a goal like that in my entire career. I was going to pass the ball but there was no one ahead of me so I just decided to go for it and see what happens”. The win left Red Star needing to win their last group match to stand a chance of qualifying for the knockout rounds, but they failed to do so.

He also scored in his next match, against Poland in another friendly, and established himself as a regular selection, but it was his substitute appearance in a crucial World Cup qualifier against Spain in Madrid in September 2005 that brought him wider international recognition. After a poor first-half – Petković said they “were lucky to be only a goal down at half-time” – Žigić was introduced, and the tactic of “putting him in the centre of the opposition defence and playing long high balls to him … was remarkably successful”. He pressured the goalkeeper into missing a cross which dropped for Dejan Stanković to set up Mateja Kežman’s equaliser, and 12 minutes later, his pass left Kežman clear on goal but he mis-hit what might have been a winning shot. The result left Serbia-Montenegro top of the group, and they confirmed their qualification at home to Bosnia and Herzegovina when Žigić’s assist gave Kežman a tap-in for the only goal of the game.

Žigić began the season with Red Star, but on 29 August 2006, he signed a four-year contract with La Liga club Racing Santander. The fee, officially undisclosed, was variously reported at anything from €4.5M to €7M. Although better offers had been rejected, those offers had arrived at the wrong time: the pressure on Red Star to win the domestic title meant they were unlikely to dispose of a major player in mid-season. The player felt he was more likely to start matches with a club at Racing’s level. Partnering the diminutive Pedro Munitis, he contributed 11 goals – including a hat-trick in a 5–4 win over Athletic Bilbao – four assists and five penalties won in league competition over the season as Racing finished tenth. The efficacy of the pair earned them the nickname of Dúo Sacapuntos (the Two Point-getters); ahead of the coming season, new coach Marcelino García Toral recalled how “we all know how many points Racing picked up when Žigić and Munitis weren’t there. Without them, Racing didn’t add points”. His performances earned him the captains’ vote as best player based abroad for 2006, and contributed to his 2007 Football Association of Serbia Golden Ball award.

Still an automatic choice under new national manager Javier Clemente, Žigić scored the only goal in Serbia’s first competitive match as a separate country, a Euro 2008 qualifier at home to Azerbaijan in September 2006. He scored once, missed two more good chances and was then sent off for elbowing an opponent in stoppage time of the March 2007 qualifying defeat in Kazakhstan, so missed the next, a home draw with Portugal, and also missed the Finland fixture in June after surgery on a facial injury. He still scored seven goals as Serbia failed to qualify.

Žigić signed for Valencia in August 2007. The fee was unconfirmed, but suggestions appeared in the media of €15M, €18M, and around €20M, a figure possibly including the player’s wages over the five years of his contract. He had been linked with numerous other moves, and Fenerbahçe made an offer that was better financially for both Racing and the player, but Žigić preferred to stay in “the best league in Europe” in a country where he was accustomed to the language and culture. He was suffering from an ankle injury when he arrived – which delayed his integration into the first-team group and, according to Mundo Deportivo, undermined the coaching staff’s confidence in him – then aggravated the injury by playing in a Euro 2008 qualifier in September, and did not appear for Valencia until October.

In the 2009 close season, there were rumours linking Žigić with moves to clubs including Sunderland, Monaco, and Bordeaux, but the player insisted his intention was and always had been to be successful with Valencia. He made 26 appearances for the club in 2009–10 in all competitions, more than in the previous two seasons combined, but only 5 were league starts. Within four minutes of replacing the injured David Villa in the league match against Racing in October, he took advantage of a defensive error to score the only goal of the game; out of respect for his former club, he did not celebrate. On 2 January 2010, his 93rd-minute header against Espanyol took Valencia third in the table, and his double against Deportivo La Coruña in the 2009–10 Copa del Rey put Valencia 2–0 up at half-time; the game finished 2–2 and Valencia lost 4–3 on aggregate. With four minutes left of the Europa League quarter-final second leg, Valencia were denied a penalty when an Atlético Madrid defender pulled Žigić to the ground so forcefully that a large hole was torn in the front of his shirt, apparently unnoticed by referee or goalline official; the tie ended goalless, so Atlético progressed on away goals from the first leg and went on to win the competition. Away to Espanyol on 1 May, again as a substitute for Villa, he scored both goals in a 2–0 win that secured Valencia a place in the next season’s Champions League.

Žigić’s extreme height predisposes him to an aerial game. He is dangerous from set pieces, scoring many headed goals and knocking the ball down for others: when he joined Red Star, the coach set out the team in a 4–3–3 formation, with Žigić at centre-forward and two wingers to feed those strengths. He tried to use his physical presence to disrupt opposing defences, both for his own benefit and to draw their attentions away from others. Pep Guardiola said in 2009 that Žigić was not easy to defend against, “almost unstoppable” in the air, but the best way would be to keep him as far as possible away from the penalty area. Speaking in 2010, Radovan Ćurčić, then assistant manager of the Serbia national team, described him as “the king of air play, he is the finest there is in Europe. He possesses the sense of space and movement without the ball and can assist his teammates with headers and set up goal-scoring opportunities.”

On 25 May 2010, Žigić signed a four-year contract with Premier League club Birmingham City for an undisclosed fee, which media speculation suggested to be in the region of £6 million. He made his debut on the opening day of the season away at Sunderland: replacing Garry O’Connor in the 58th minute, he came close to scoring from outside the penalty area and “injected a note of panic hitherto undetected” in the home team’s defence as Birmingham came back from 2–0 down to secure a draw. Žigić’s first goal for the club came as Birmingham beat Milton Keynes Dons 3–1 in the League Cup on 21 September. He scored his first Premier League goal on 16 October, opening the scoring at Arsenal with a header from Keith Fahey’s cross, but Birmingham lost the game 2–1.

Goals in four of Serbia’s five internationals in the latter part of 2010 brought his total to 20. He was not selected to start the other match, a Euro 2012 qualifier in Italy that was abandoned after six minutes because of crowd trouble; UEFA awarded the match to the hosts as a 3–0 win. After Serbia failed to qualify for the tournament, both Stanković and Nemanja Vidić retired from international football, and Žigić was appointed captain of the national team. He captained the team in friendly defeats to Mexico and Honduras in 2011, his 56th and 57th appearances for his country, which proved to be his last.

He prefers to receive the ball in the air, because he can always beat smaller players in the air but they can take advantage of better acceleration and quicker reactions on the ground. According to David Pleat, a major factor in Birmingham’s 2011 League Cup win was “telling him to do what he does best and flick the ball on with his head from direct diagonal balls played from both wings”. Nevertheless, he is technically competent, scoring goals with his feet and providing assists for others. A 2009 feature in Mundo Deportivo assessed Žigić as one of those few tall players with a good touch on the ball, and in 2010, German international defender Per Mertesacker described him as “technically a good player and very smart tactically”.

Having been without a club since his departure, Žigić began training with Birmingham again in November 2014. After a successful appeal to be granted a work permit, for which he did not qualify automatically, he signed a contract on 4 December to expire at the end of the season. He made his second debut as a late substitute in the Championship match at home to Reading on 13 December, with Birmingham already 6–1 ahead. He played only infrequently – nine substitute appearances in the league and two FA Cup matches – and the club confirmed he would be released when his contract expired.