The Spaniard completed his move to the Italian champions from Real Madrid on Saturday but limped out of training with his new team-mates just two days later.
After undergoing tests, Juve confirmed on Tuesday the 21-year-old had suffered a second grade tear of the medial collateral ligament in his left knee.
As a result, the Spain Under-21 international faces around seven weeks out of action and looks set to miss all of Juve's pre-season preparations.
"Alvaro Morata this morning underwent an MRI scan after being forced to depart yesterday afternoon's training session early due to injury," read a statement on the club's official website.
"The tests, carried out at Turin's Clinica Fornaca di Sessant, revealed a second grade tear of the medial collateral ligament in the striker's left knee.
"He is estimated to return to action in 50 days."
