Born in Wodonga, Victoria, Kennedy began playing junior football in Albury/Wodonga, near his hometown of Yackandandah in Victoria, Australia. There, he played with the Twin City Wanderers and later SS&A Boomers. His talents won a scholarship place in the Australian Institute of Sport program, leading to a professional contract at new National Soccer League club Carlton in 1999, alongside fellow AIS graduates Vince Grella and Mark Bresciano.

In 1999, Kennedy represented Australia at the U17 World cup and the Young Socceroos in 2001 at the U20 Youth World Cup in Argentina.

After a season, he made a move to Europe transferring to Bundesliga club VfL Wolfsburg. His debut as a substitute coming on five minutes from time in the 4–4 draw against fellow Northern German side Hamburger SV on 13 September 2000, at age 17 made him the youngest player ever to appear for VfL. It was his only appearance for the first team that year, and the following season brought little change for Kennedy as he managed just seven appearances for the Bundesliga side, starting only once. However, he scored two goals in the 2001–02 season, with his first ever Bundesliga goal coming on 8 September 2001 against Energie Cottbus.

In July 2006, during his first training session with Nürnberg, Kennedy ruptured his right Achilles tendon.

Injury prevented Kennedy from participating in Australia’s 2007 AFC Asian Cup campaign. Kennedy was recalled to the Socceroos squad to face Argentina in a friendly on 11 September. On 6 February 2008, he scored his second international goal against Qatar in a World Cup qualifier held in Melbourne, his third against South Africa, fourth against Holland and his fifth against Qatar again. On 1 April 2009, he scored his sixth goal for Australia, Kennedy came on as a substitute on the 60th minute for Scott McDonald and scored a header against Uzbekistan giving Australia a 1–0 lead.

On 11 January 2008, fellow German Bundesliga club Karlsruher SC announced the signing of Kennedy via an undisclosed transfer fee. He is contracted until June 2011. His first goal for Karlsruhe came on his debut against his former club Nürnberg in what would turn out to be a cruel twist of fate for the latter – just weeks after leaving them. Kennedy went on to score four goals in his first five appearances and was widely praised for his performances. However, following this stunning start he did not manage to score in 21 consecutive Bundesliga matches and finally lost his starting position. After a further disappointing appearance in an important cup tie on 28 January 2009, Kennedy was replaced in the second half of the match and subsequently refused to shake hands with his coach. Due to this behaviour, he was thrown out of the squad. On 2 February 2009, Kennedy once again made negative headlines when he announced his intention to leave the club as soon as possible. After five months without any Bundesliga appearances Kennedy was finally allowed to return to the squad even though he still refused to apologise. On 18 April 2009, he was part of the starting line-up for the first time since his suspension. Altogether, Kennedy started 20 of his 23 appearances but – after 27 goalless games – was only able to score twice in the final match of the season which proved to be of no relevance because Karlsruhe nevertheless was relegated from the Bundesliga.

On 17 June 2009, he signed a contract with Nagoya Grampus until 31 December 2011. Kennedy scored a goal on debut for Nagoya Grampus in his side’s 1–1 draw. In the 2010 season, Kennedy helped Nagoya win their first-ever league title, becoming a joint top scorer with Ryoichi Maeda on 17 goals. He was also named in the 2010 J. League Best Eleven. On 23 September 2011, Kennedy scored off a Kensuke Nagai cross to help his side to a 3–1 win over Vissel Kobe. The result put Grampus one point behind leaders Gamba Osaka and gave Kennedy his 15th goal of the 2011 J. League season, putting him one goal above Ventforet Kofu’s striker Mike Havenaar. Kennedy finished the season with 19 goals and the J-league golden boot.

His most important goal, however, came in Australia’s last World Cup qualification match on 18 June 2013. After not earning a game for over a year, he came on as a 77th-minute substitute for Tim Cahill and scored Australia’s only goal against Iraq with an 83rd-minute header to secure a win and a spot in the World Cup finals.

On 6 November 2014, it was announced that he had signed with Melbourne City as their Australian Marquee. He joined the team in January 2015. Kennedy debuted for City against Melbourne Victory, being substituted on the field for Safuwan Baharudin in the 60th minute. He opened his scoring account for City with their second goal in the clinical 3-2 win over Adelaide United. He added a second goal to his record with a composed finished against the Wellington Phoenix in their Finals eliminations clash.

Kennedy was selected for the Brazil 2014 World Cup squad, after his goal qualified Australia for the tournament. On 4 June 2014, at the socceroos’ training camp near Rio, Kennedy was cut from the team due to injury.

Kennedy announced his retirement from professional soccer on 26 June 2015 due to persistent injuries. Kennedy finished his career with a J-League Championship, two J-League Golden Boots, a DFB Pokal Cup and 17 international goals for the Socceroos across three World Cup campaigns.