The San Siro side have been dealt yet another injury blow as the attacking midfielder will be out for around a month
The Brazilian was forced to leave the pitch after 70 minutes of play during his Milan return in the 2-2 Serie A draw against Torino on Saturday evening.
"AC Milan communicate that medical examinations have revealed an injury to Kaka's left adductor," read a statement from Milan.
"The player will undergo another series of tests in 10 days before making a prognosis about the date of return."
Kaka, meanwhile, has made it clear that he will waive his right to receive his wages as long as he is unavailable due to injury.
"Saturday was a bad day for me as I didn't expect this," the 31-year-old told Milan Channel.
"I've talked about this with the club and with [CEO] Adriano Galliani. What I have decided is that I don't want the club to pay me while I'm unavailable. All I want is the club's support and affection during my absence."
Milan have a number of first-team players injured with Giampaolo Pazzini, Daniele Bonera, M'Baye Niang, Riccardo Montolivo, Mattia De Sciglio, Ignazio Abate and Stephan El Shaarawy also sidelined for the clash against Neil Lennon's side at San Siro.