The Rossoneri pair will spend up to three weeks on the sidelines, as the Italy midfielder contracted a muscle strain, while the Ghanaian's hand was operated on
The Italy international suffered a knock to his right thigh, after being hauled off in Saturday's 3-1 victory over Bologna, and should be back in approximately 20 days time.
Boateng, meanwhile, underwent an operation on his right hand on Monday, having broke a third metacarpal bone, and is expected to be back within three weeks.
The Rossoneri are already without the services of Alexandre Pato, Robinho and Ignazio Abate, who are all currently enduring spells on the treatment table.
However, Massimiliano Allegri's men returned to winning ways over the weekend at the Dall'Ara, and now sit 10th in Serie A after two matches.