The 22-year-old will be out with a thigh injury picked up in last week's Coppa Italia win over Novara.
The Brazilian has played in the majority of Milan's games this season, helping them reach second in the table - just a point behind leaders Juventus.
The Serie A side play seven games during the four-week period, including their crucial UEFA Champions League encounter with Arsenal on 15th February.
Pato looks set to miss the game at the San Siro, but should be available for the return leg at the Emirates in March.
He could also be involved in what could be a title-decider against Juventus on 25th February.
A statement on the club's official website read: "The prognosis is three/four weeks, unless there are complications."