Born in Orléans, Thauvin played for youth teams at Ingre, Saint-Jean-de-la-Ruelle, Orléans, and Grenoble before rising through the ranks at the latter, and drawing the interest of larger clubs. He made his first team debut for Grenoble on 11 March 2011 in a 1–1 Ligue 2 away draw against Vannes. Grenoble was relegated to the CFA 2 after its liquidation in July 2011.

On 19 July 2011, Thauvin departed the club and signed his first professional contract with Corsican side Bastia. On 28 October 2012, he scored his first goal for Bastia in a 3–1 victory over Bordeaux. He helped Bastia to Ligue 2 title triumph in 2012.

On 29 January 2013, Thauvin signed a four-and-a-half-year deal with Ligue 1 club Lille for a reported fee of €3.5 million. As part of the deal, he was immediately sent back to Bastia on a six-month loan deal, keeping him at the top-flight Corsican club until the end of the 2012–13 season. Following his impressive displays that season, Thauvin was named the Ligue 1 Young Player of the Year.

On 3 September 2013, after weeks of drawn-out negotiations and without making single appearance for Lille, Thauvin signed a five-year deal with Olympique de Marseille. The 20-year-old had been absent from training due to disputes over an improved contract, and forced a move to the Stade Velodrome, eventually signing for €15 million including bonuses.

In January 2014, he was named by The Observer as one of the ten most promising young players in Europe. Former Toulouse manager Alain Casanova called Thauvin “a player in the image of Franck Ribéry … someone who is able to disrupt any opponent, someone very dangerous when he picks up speed. Very dangerous indeed.” ESPN columnist Andy Brassell described him in 2013 as a wide player who is a “left-footer with fine acceleration and jaw-dropping close control.”

On 4 January 2015, Thauvin was the only Marseille player to miss in the penalty shootout as they were eliminated from the Coupe de France last 64 by fourth-tier former club Grenoble. Thauvin made 81 appearances over two seasons, scoring 15 goals.

On 19 August 2015, Thauvin joined Newcastle United signing a five-year deal, for a reported fee of £15 million, with Rémy Cabella going in the other direction to Marseille on a season-long deal, with an option to buy. Thauvin was handed the departing Cabella’s number 20 shirt. He made his debut three days later, replacing compatriot Gabriel Obertan, in the 69th minute of a goalless draw against Manchester United at Old Trafford, a game in which he had a chance to score a winner, but he was unable to reach a cross. He made his first start for the club against Northampton Town in the League Cup second round on 25 August, scoring a goal and making three assists in a 4–1 home victory.

Thauvin was criticised by Newcastle’s all-time top scorer Alan Shearer for turning up to a game wearing a tuxedo. In February 2016, he told L’Équipe that the criticism was unfair and affected his performances.

On 31 January 2016, Newcastle announced Thauvin would return to Marseille on loan for the rest of the season. In the first game of his loan, on 2 February, he was sent off ten minutes after coming on as a substitute at Montpellier for a foul on Hilton. He scored the only goal on 20 April as they beat FC Sochaux-Montbéliard 1–0 away in the semi-finals to reach the final of the 2016 Coupe de France against Le Classique rivals Paris Saint-Germain, which they lost 4–2 with Thauvin scoring a goal.

On 4 August 2016, Thauvin began his second loan spell at Marseille, signing a season-long loan deal; Newcastle inserted a clause in the contract which gave Marseille the option to make the deal permanent. In November 2016, it was reported that the loan spell would be made permanent in the summer of 2017, with Marseille agreeing to pay £9.8 million (€11m) for Thauvin’s permanent transfer once he had played just three matches for the club during his second loan spell.

Thauvin captained Marseille for the first time in the 2016–17 Coupe de France round of 64 away match against Toulouse on 8 January 2017, which Marseille won 2–1. On 10 March, he scored two goals in the 3–0 Ligue 1 home win over Angers, taking his tally to four goals in his last four Ligue 1 matches. He was the UNFP Player of the Month for March, with three goals and two assists. On 30 April, Thauvin scored the first hat-trick of his senior club career and assisted one of Maxime Lopez’s two goals in a 5–1 Ligue 1 away win over Caen.

On 2 February 2018, Thauvin scored another hat-trick in a 6–3 home win over Metz. He won two more Player of the Month awards for November and February, and finished the 2017–18 Ligue 1 season with 22 goals, behind only PSG’s Edinson Cavani for top scorer. He was one of four candidates for the Player of the Season award, that ultimately went to the Parisians’ Neymar. In the season’s Europa League, he contributed four goals in fourteen games for the team, who lost the final to Atlético Madrid in Lyon.

Thauvin was called up to the senior France squad for the first time to face Luxembourg in a 2018 World Cup qualifying match on 25 March 2017 and Spain in a friendly three days later; he did not play in either match. On 2 June 2017, Thauvin made his debut for Les Bleus in a 5–0 friendly win over Paraguay, coming on in the 80th minute as a substitute for Antoine Griezmann.

In 2018–19, Thauvin was Ligue 1’s fourth-highest scorer with 16 goals in 33 games, though Marseille finished fifth and missed out on European football; his tally included a hat-trick in a 3–1 win at Amiens on 25 November. He was sent off two months later in a 2–1 home loss to Lille. In September 2019, he was ruled out with ankle ligament injury, returning in March only for the season to be abandoned due to the coronavirus pandemic. On 13 September 2020, Thauvin scored the only goal of an away win against Paris Saint-Germain, to grant Marseille their first win in Le Classique since November 2011.

On 11 June 2019, Thauvin scored a bicycle kick (his first senior international goal) in the 4–0 away win over Andorra in a UEFA Euro 2020 qualifying match, after having assisted Wissam Ben Yedder’s goal 16 minutes earlier.