The Rossoneri hope the midfielder returns to action swiftly after picking up a muscular problem against Udinese for Juventus at the weekend
The 34-year-old was substituted in the first half as the Bianconeri beat Udinese 1-0 and, on Monday, it was confirmed that the Italy international had damaged the medial ligament in his right knee.
Although no official return date has been given, Pirlo is expected to be out until at least the middle of January and the Rossoneri - whom he left in 2011 on a free transfer - expressed their hope that he returns to action in Italy quickly.
"Everybody at Milan, from the players to the coaching staff, would like to send their regards to Andrea Pirlo and wish him a speedy recovery with his knee injury," the San Siro side said in a statement on their website on Tuesday.
Pirlo's fitness woes mean he will not feature in Juve's crunch Champions League tie with Galatasaray on December 10, when the team need at least a draw at the Turk Telekom Arena to qualify for the last 16 of the competition behind Real Madrid in Group B.
Next up, though, is a trip to Bologna on Friday as they hope to extend their three-point lead over second-placed Roma in Serie A.