Moura joined São Paulo FC in 2005 after playing for the youth teams of Clube Atlético Juventus and Corinthians and was known as Marcelinho since he played for a Marcelinho Carioca football school as a child and also had physical resemblance with the former footballer. Having had prominence at youth level, he was promoted to play professionally by Milton Cruz. Moura made his debut with the São Paulo first-team in 2010, scoring 4 goals and providing four assists in 25 appearances. In the same year, he stated his desire to be known for his given name instead of a nickname to “make his own history in football without comparisons”. In 2011, Moura scored nine goals and provided four assists in 28 appearances in the Campeonato Brasileiro and 13 goals and eight assists in all competitions.

Moura was a frequent member of Brazil’s Under-20 international side. In February 2011, he was involved for Brazil in the Under-20 South American Championship where he scored a hat-trick in a 6–0 victory over Uruguay in the final. Moura made his senior international debut for Brazil in friendly match against Scotland on 27 March 2011. On 28 September 2011, Moura scored his first senior international goal for Brazil against Argentina.

During the summer of 2012, both Manchester United and Inter Milan were reported to be interested in signing Moura. On 8 August 2012, Paris Saint-Germain won the battle and announced the player would be moving to the club in January 2013. He would be the club’s most expensive signing. The transfer fee was reported to be in the region of €45 million (£38 million). It was announced that Moura would wear the No. 29 shirt for the remainder of the season.

Moura was selected to compete for the Brazil Olympic football team in the 2012 Summer Olympics in London along with club teammates Casemiro and Bruno Uvini. He appeared in three matches as a substitute, including the Gold medal match with Mexico, and started in the 3–0 group stage victory over New Zealand.

On 11 January 2013, Moura made his debut against AC Ajaccio, in a match that ended as a 0–0 draw. He also played in the Champions League away victory over Valencia on 12 February, assisting a goal in the process. On 13 September 2013, he scored his first goal for PSG in a 2–0 league victory over Bordeaux.

For the 2014–15 season, following Jérémy Ménez’s transfer to A.C. Milan, Moura was handed the No. 7 shirt – the same number he wore while playing for São Paulo. He made his season debut for PSG in their 2–0 Trophée des Champions victory over Coupe de France winners EA Guingamp on 2 August 2014 at the Workers Stadium in Beijing.

On 7 August 2015, Moura scored the first goal of the 2015–16 Ligue 1 season in PSG’s 1–0 defeat of Lille OSC at the Stade Pierre-Mauroy.

On 15 October 2016, Moura scored PSG’s first goal in the 13th minute in a 2–1 away win against AS Nancy in a Ligue 1 match with a curling free-kick from the left which nobody got a touch to; that was his fifth league goal of the 2016–17 Ligue 1 season. For the 2017–18 Ligue 1 season, he appeared only as substitute six times for the club, and left in January 2018.

In 2016, Moura was named in Dunga’s 23-man squad for the Copa América Centenario in the United States.

On 31 January 2018, Moura signed a contract with Tottenham Hotspur until 2023 for a transfer fee of around £25 million. He made his debut for Tottenham in the 2017–18 UEFA Champions League match against Juventus on 13 February 2018, coming on as a late substitute in the match that ended in a 2–2 draw. He made his first start as well as scoring his first goal for the club in the FA Cup tie against Rochdale on 18 February 2018 that also finished 2–2.

In the 2018–19 season, Moura scored his first Premier League goal on 18 August 2018 in Spurs’ 3–1 win over Fulham. In the following match on 27 August 2018, he scored a brace against Manchester United as Tottenham won 3–0 in only their third away win at Old Trafford in 27 games. He scored his first Champions League goal for Spurs in the group round match against PSV. In the away match against Barcelona at Camp Nou, Moura scored a late equaliser after Barcelona took an early lead in the game. The game ended 1–1, which sent Tottenham through into the knockout stage together with Barcelona. On 13 April 2019, he scored a hat-trick in the 4–0 win over Huddersfield Town. This was his first hat-trick in Europe and the first ever hat-trick scored at the new Tottenham Hotspur Stadium.

On 8 May 2019, Moura scored a second half hat-trick in Tottenham’s 3–2 victory over Ajax at the Johan Cruyff Arena in the second leg of their Champions League semi-finals. Spurs came back from 2–0 down on the night, and 3–0 down on aggregate to win on away goals. His third goal, in the 96th minute, sent his team into a Champions League final for the first time in their history. This performance lead L’Équipe to award him a perfect 10 rating, making him the tenth ever player to be awarded a 10 rating by them.

On 9 August 2019, Moura signed a new contract with Tottenham until 2024. He scored his first goal of the 2019–20 season on 17 August 2019, equalising against Manchester City within nineteen seconds of being introduced as a substitute.