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."
The injury represents a blow for Morata as well as new Juve coach Massimiliano Allegri, who replaced Antonio Conte earlier this month.
Allegri, sacked by Milan in January, will be tasked with continuing the work of Conte - who won three Scudetti during his time at the helm.
