Donnarumma grew up in the football academy of ASD Club Napoli in his native Castellammare di Stabia, which he joined in 2003. In 2013, at the age of 14, he was signed for €250,000 by Milan, the team for which his elder brother, Antonio, had already played. Between 2013 and 2015, he was part of the Rossoneri youth academy, where he always played in the age group above him, beginning with the Giovanissimi, then the Allievi, and finally the Primavera. Three days before his 16th birthday, in February 2015, he received his first call-up to the senior team from manager Filippo Inzaghi; though he did not feature in the league match against Cesena, his presence on the substitutes’ bench had required a special dispensation due to his age. In March 2015, Donnarumma signed his first professional contract with Milan, effective from 1 July 2015 until 30 June 2018.

A 2015 ESPN profile praised Donnarumma’s fundamental goalkeeping skills, identifying his large slender frame and reach, agility, and composed nature as his biggest strengths; writer Nick Dorrington additionally described the teenager as “a natural leader [with] the necessary confidence to organise a defence featuring players twice his age.” Despite his tall and imposing stature, Donnarumma possesses good reactions, and is effective at stopping penalties. Matt Jones has also praised Donnarumma for his shot-stopping ability, and speed when rushing off his line to face opponents in one on one situations. Former Milan goalkeeper Christian Abbiati touted Donnarumma as a potential future captain for Milan in 2016, noting that Donnarumma’s temperament, introverted character, and ability to withstand pressure were all the necessary qualities needed for him to succeed in this role. Although Donnarumma is regarded as being competent with the ball at his feet, pundits such as Mina Rzouki, Paolo Menicucci, and Sam Lopresti, as well as former goalkeeper Fernando Orsi, have cited his ball control and distribution, as well as his overall consistency, positioning, handling, punching technique, and his ability to defend crosses and command his box as areas in which he needs to improve as he gains more experience.

In the club’s opening league match of the 2016–17 season against Torino, on 21 August, Donnarumma saved the first penalty of his professional career; he stopped Andrea Belotti’s shot in injury time, which enabled Milan to seal a 3–2 victory at home. He kept his first clean sheet of the season in the 1–0 victory against Sampdoria on 16 September. On 23 December, Donnarumma helped lead Milan to victory in the Supercoppa Italiana, saving Paulo Dybala’s penalty in a 4–3 shoot-out win following a 1–1 draw after extra time. On 15 June 2017, it was initially announced that Donnarumma would not be renewing his contract with Milan, however on 11 July, after much speculation, he renewed with Milan until 2021.

Donnarumma played his first European game in a 1–0 win against CS U Craiova in the first leg of Milan’s Europa League third-round qualification match on 27 July 2017, in which he managed to keep a clean sheet. He also kept another clean sheet in the second leg the following week, as Milan beat their opponent 2–0. He kept his third consecutive clean sheet in the competition in Milan’s 6–0 win against Shkëndija in the first leg of the play-off round. He kept another clean sheet in his first match in new Serie A season against Crotone. On 30 December 2017, Donnarumma played his 100th game for Milan in a 1–1 draw against Fiorentina; becoming the youngest player to make 100 appearances with Milan’s jersey. On 28 February 2018, following a 0–0 aggregate draw after extra-time, Donnarumma saved two penalties in a 5–4 shoot-out victory over Lazio in the second leg of the Coppa Italia semi-finals in Rome, which allowed Milan to advance to the final of the competition. On 15 April 2018, Donnarumma became the youngest player to reach 100 appearances in Serie A, aged 19 years and 49 days, after a 0–0 home draw against Napoli. On 9 May, Donnarumma started in Milan’s 4–0 defeat to Juventus in the Coppa Italia final, who won their fourth consecutive title.

Though predicted to attend the 2016 UEFA European Championship, Donnarumma did not make Antonio Conte’s final squad for the tournament. On 27 August, he was called up to the senior squad by Gian Piero Ventura for a friendly against France on 1 September and a 2018 World Cup qualification match on 5 September against Israel, making him the youngest player, aged 17 years and six months, to be called up to the senior squad since 1911. On 1 September, in the match against France, Donnarumma made his senior debut, subbing out Gianluigi Buffon at the half-time mark of a 3–1 home loss; the youngest goalkeeper to ever play for Italy aged 17 years and 189 days. On 28 March 2017, he made his first starting appearance in a 2–1 away win over the Netherlands; the youngest goalkeeper for Italy to do so aged 18 years and 31 days.

In June 2017, he was included in the Italy under-21 squad for the 2017 UEFA European Under-21 Championship by manager Luigi Di Biagio. Italy were eliminated in the semi-finals following a 3–1 defeat to Spain on 27 June.

Widely regarded as the heir of Buffon, following the international retirement of the latter in 2018 Donnarumma was chosen as the first-choice goalkeeper by the new head coach Roberto Mancini and played as a starter in all the matches of the 2018–19 UEFA Nations League disputed by the Azzurri.

Following the arrival of Pepe Reina during the 2018–19 season, manager Gennaro Gattuso announced that the two goalkeepers would share the role of starting goalkeeper across the club’s competitions, with Donnarumma starting in Serie A, while Reina started in the Europa League. On 3 February 2019, Donnarumma was named man-of-the-match in Milan’s 1–1 away draw with Roma in the 21st Round of the 2018–19 Serie A season, making five important saves. On 10 February, he made his 150th Milan appearance in a 3–0 home win over Cagliari in Serie A; as a result he became Milan’s tenth-most capped keeper of all time, behind Christian Abbiati (380), Sebastiano Rossi (330), Dida (302), Lorenzo Buffon (300), Enrico Albertosi (233), Dario Compiani (221), Fabio Cudicini (183), Giovanni Rossetti (180), and Mario Zorzan (176).

During the 2019–20 season, Donnarumma maintained his place in the starting line-up. On 21 July 2020, he played his 200th game for the club in a 2–1 away win over Sassuolo in Serie A, during which he wore the captain’s armband for the first time in his career, after Alessio Romagnoli was subbed off due to injury.

On 26 October 2020, Donnarumma tested positive for COVID-19 amid its pandemic in Italy.