The attacking midfielder was forced to leave the pitch after 70 minutes of play on his Milan return and underwent further examination on Monday to clarify the extent of his injury.
“AC Milan communicate that medical examinations have revealed an injury to Kaka’s left adductor,” a Milan statement reads.
“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.
“You have probably read about my injury on the Milan website,” the attacking midfielder said in a video message to fans.
“Yesterday was a bad day for me because in all honesty I was not expecting an injury like this. It was really bad and difficult for me.
“I have spoken at length with the club, with [Vice-President Adriano] Galliani and with the doctors to decide on a few things.
“In the end I decided that I don’t want anything from Milan except for love and support until I am better, until I am fully fit and ready to play again.
“For this reason, I have decided to suspend my current pay for this period of time. The only thing I ask is for support and help to recover properly.
“I have already started my rehabilitation and I have to say that your support and everything I have heard over the last few days really drives me on and makes me determined to come back as soon as possible.
“It is a difficult moment, but I have started to work on getting better and I hope to be back as quickly as possible to bring some joy to all you fans out there and to myself too.”
The recent Gazzetta dello Sport salary report claimed that Kaka was on €4m a season after tax. If that figure is accurate then the new Milan captain will be sacrificing around €307,000 should he be out for four weeks.