Maldini was born in Milan, the second son of Paolo Maldini, then captain of AC Milan, and Venezuelan model Adriana Fossa. His grandfather Cesare also captained Milan in the 1960s, making him the third generation to make appearances for the club. His elder brother Christian played for Milan's youth teams and went on to play professionally at a lower level.
Maldini joined Milan's youth system in 2010, and over the following years he came through the various age-group teams, from the under-10 Pulcini to the under-19 Primavera. In the 2016–17 season, he was part of the squad that won the Under-16 National Championship (Campionato Nazionale Under-16), defeating Lazio 5–2 in the final.
On 2 February 2020, Maldini made his senior debut with Milan in a 1–1 Serie A home draw against Hellas Verona, coming on as an added-time substitute for Samu Castillejo.
On 15 September 2021, Maldini came off the bench against Liverpool in a 3–2 defeat on his UEFA Champions League debut. On 25 September, Maldini started his first match for Milan in Serie A and scored the first goal in a 2–1 away win against Spezia.