The extent of the injury will be announced in the next few days but it is clear that the 22-year-old will miss some, if not all, of the Rossoneri's push for Champions League qualification.
The former Barcelona player had been complaining of discomfort for a few days and both the club and player took to social media to announce the bad news after further investigation.
"The tests confirm a breakage to the quadriceps. I'll do anything to get back as soon as possible," tweeted the Spanish striker.
"Bojan Krkic has sustained an injury to his right rectus femoris," read a club statement on Twitter.
The former Barcelona player is at Milan on-loan from Roma but still has a buy-back clause in his contract for a move back to Camp Nou.
AC Milan sits in third place in Serie A with just a one-point cushion ahead of fourth-placed Fiorentina and takes on Torino at San Siro on May 5.