The Brazilian forward picked up the muscle complaint in the opening defeat to Sampdoria in Serie A on Sunday.
The forward was replaced by Urby Emanuelson towards the end of his side's 1-0 reverse to Sampdoria on Sunday, in the opening weekend of the new Serie A season.
A statement on the Rossoneri's official website has revealed the 28-year-old suffered a strain to his right thigh, and is expected to return within the next four weeks, barring any complications.
Robinho's injury blow may have contributed to the club's late surge in transfer activity, with Bojan Krkic set to follow Giampaolo Pazzini and M'Baye Niang to San Siro before the August 31 deadline.
Follow GOAL.COM USA on