The former Chelsea striker collided in the air with centre-back Strahinja Pavlovic and was quickly transported to a hospital in Legnano for medical attention.
Morata was given an all-clear after undergoing an MRI scan but remained in hospital for observation.
The Spain international will now miss AC Milan’s Serie A match away to Cagliari on Saturday.
Former Chelsea striker Tammy Abraham is expected to deputise in Morata’s absence.
On Tuesday, Morata scored against his former club as AC Milan ran out 3-1 winners against Real Madrid in the Champions League at the Santiago Bernabeu.
‘I told the guys beforehand that it’s an important match, especially for us, but also for the fans and the club,’ Morata said after AC Milan’s win against the Champions League holders.
‘We had to fight like lions, we played a great game, a serious performance.
‘We were very lucid with the ball at times and suffered together in other moments, as we had to do.’
The 32-year-old has scored three goals in 12 appearances since joining AC Milan from Atletico Madrid in a €13 million (£10.9m) in the summer.
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