The Brazilian player hurt his thigh during Saturday's 3-1 Serie A defeat at Napoli and was replaced by Kaka at half-time.
A statement from Milan read: "Robinho has sustained a muscular injury in his left thigh.
"The Brazilian striker will undergo further tests next week."
The 30-year-old has scored three goals in 18 league appearances for the Rossoneri this season.
Milan will be hoping Robinho can recover in time for the return leg against Atletico at the Vicente Calderon on March 11.