Kean was first noticed by Renato Biasi, who inserted him in the youth teams of Asti before offering him to Torino. In 2010, however, instead of renewing with the Granata, he was signed by Torino’s cross-city rivals Juventus (until a player is of 14 years of age, the contract is annual and in constant renewal). In his final season in the Juventus youth teams, in 2015–16, he scored 24 goals in 25 games.

Since 2015, Kean has represented Italy at under-15 level. With the Italy U17 team he took part at the 2016 and 2017 editions of the UEFA European Under-17 Championship, scoring 1 goal in each tournament.

Kean made his professional debut for Juventus on 19 November 2016, at the age of 16 years, 8 months and 23 days, coming on in the 84th minute for Mario Mandžukić in a 3–0 win over Pescara in Serie A. Upon doing so, he became the club’s youngest-ever debutant and the first player born in the 2000s to compete in one of Europe’s four major leagues. On 22 November, he became the first player born in the 2000s to feature in a UEFA Champions League match, after being substituted on in the 84th minute of a 3–1 away win over Sevilla. On 27 May 2017, Juventus’ final match of the 2016–17 Serie A season, Kean scored his first goal for Juventus, the winning goal of a 2–1 away victory over Bologna, also becoming the first player born in the 2000s to score a goal in one of Europe’s five major leagues.

On 31 August 2017, after extending his contract until 30 June 2020, Kean was loaned to Hellas Verona on a one-year deal. On 10 September he made his debut for Verona in Serie A as a substitute, replacing Alex Ferrari in the 46th minute in a 5–0 home defeat against Fiorentina. On 1 October, Kean scored his first goal for Verona in the 87th minute of a 2–2 away draw against Torino.

On 28 January 2018, Kean scored his first career Serie A brace in a 4–1 away win against Fiorentina, becoming only the second player born in the 2000s after Pietro Pellegri to have done so. He totalled 20 competitive appearances and four goals in his season at the club.

With the Italy U19 he took part in the 2018 UEFA European Under-19 Championship, and scored in the group stage against Norway and in the semi-final against France in a 2–0 win to help Italy reach the final of the tournament. He started the final against Portugal on the bench, but came on as a substitute and scored 2 goals in the second half, to take the tie to extra time, but the match ended in a 4–3 victory for Portugal.

He made his debut with the Italy U21 team on 11 October 2018, in a friendly match lost 1–0 against Belgium in Udine. He scored his first goal with the U21 side in the following friendly match, a 2–0 home win against Tunisia on 15 October 2018. He took part in the 2019 UEFA European Under-21 Championship, where Italy U21 has been eliminated in the group stage.

In November 2018, Kean was called up to the Italy senior side by manager Roberto Mancini. On 20 November, aged 18 years, 265 days, he made his senior debut with the Italy national team in a friendly match against the United States in Genk, which eventually ended in a 1–0 victory. On 23 March 2019, Kean made his first start and scored his first goal for Italy in a 2–0 home win over Finland in Italy’s opening UEFA Euro 2020 qualifying match. In doing so, he became the youngest forward to start a match for Italy since Edoardo Mariani started against France in 1912; Kean is currently either the fourth or fifth-youngest forward ever to start a match for Italy, behind only Mariani, Leopoldo Conti, Eugenio Mosso, and possibly Rodolfo Gavinelli, as it is not known officially whether the latter was born in 1891 or 1895. Kean also became the youngest player to score for Italy since Bruno Nicolè, who scored twice in a 2–2 friendly away draw against France on 9 November 1958; overall, Kean is the second-youngest goalscorer for Italy, behind Nicolè, at the age of 19 years and 23 days, and the youngest player to score a goal for Italy in both a competitive match, and in a European qualifier. On 26 March, he then scored his second international goal in Italy’s following Euro 2020 qualifier, a 6–0 home win over Liechtenstein.

On 12 January 2019, Kean scored in a 2–0 away win over Bologna in the Coppa Italia. On 8 March 2019, Kean scored two goals in the first half against Udinese, of an eventual 4–1 home win. On 2 April 2019, Kean scored the second goal in a 2–0 away win against Cagliari, during which Kean was subject to racist chants from a section of Cagliari fans. Juventus teammate Leonardo Bonucci was heavily criticised after stating that Kean was partly to blame by his celebration which caused further jeers, by England international Raheem Sterling who deemed the comments ‘laughable’, compatriot Mario Balotelli, English rapper Stormzy, and former Juventus player Paul Pogba. Bonucci implied that Kean’s celebration caused further jeers, stating to Sky Sport Italia: “Kean knows that when he scores a goal, he has to focus on celebrating with his teammates. He knows he could’ve done something differently too. There were racist jeers after the goal, Blaise heard it and was angered. I think the blame is 50–50, because Moise shouldn’t have done that and the Curva should not have reacted that way. We are professionals, we have to set the example and not provoke anyone.” In Juventus’s following match on 6 April, Kean came off the bench against Milan to score the winning goal in a 2–1 home win in Serie A, putting his side just one victory away from winning the league title. The following league match, on 13 April, Kean scored the first goal in a 2–1 away defeat against SPAL, marking his sixth consecutive goal in as many matches for club and country.

Kean joined Everton on 4 August 2019, signing a five-year contract for a fee of €27.5 million, plus €2.5 million in add-ons. On 10 August, he made his Everton debut in a 0–0 draw against Crystal Palace in the Premier League, coming on as a substitute for Dominic Calvert-Lewin. In November 2019 Kean was dropped from Everton’s match-day squad for disciplinary reasons. Kean scored his first goal for Everton on 21 January 2020, in a 2–2 home draw against Newcastle United in the Premier League. For the last game of the season Kean was handed a start and scored his second goal for Everton, equalising against A.F.C Bournemouth in the 41st minute, a game Everton went on to lose.

Kean began the 2020–21 season at Everton, and scored two goals in two EFL Cup matches. On 4 October 2020, he joined Ligue 1 club Paris Saint-Germain in a one-year loan. He made his debut in a 4–0 away win against Nîmes in Ligue 1 on 16 October; he did not score a goal, but saw a headed attempt ricochet on the crossbar. In the following league game on 24 October, Kean’s first goals for the club came in the form of a brace against Dijon, in a 4–0 win. On 28 October, in Paris Saint-Germain’s next game, Kean scored his first UEFA Champions League goals, scoring a brace against Turkish club İstanbul Başakşehir in the group stage.