The Italy international was substituted in the second half of the first leg of the Rossoneri's Champions League last 16 tie with Atletico Madrid on Wednesday.
Milan has now confirmed that the forward will miss Sunday's Serie A trip to Sampdoria on Sunday and faces a race against time to be fit to face leader Juventus seven days later.
A club statement released Thursday read: "AC Milan wishes to communicate that in yesterday evening's match [against Atletico], Mario Balotelli suffered a shoulder injury. The player visited with professor Alessandro Castagna today [Thursday] and the recovery time has been estimated at around 10 days without unforeseen complications.
"Mattia De Sciglio also suffered an ankle injury in yesterday’s match and the player's recovery time will be decided on in the coming days based on medical tests."
Milan was beaten 1-0 by Atletico, with Diego Costa heading home the winner at San Siro with just seven minutes to go.