The 21-year-old, who completed his move from Real Madrid on Saturday, suffered a second degree injury to the medial collateral ligament in his left knee after being injured on Monday, the Serie A champions said in a statement on Tuesday.
"The forecast for a full recovery is of 50 days," the club said.
A highly-rated product of the Real youth academy, Morata came to the fore in the 2012-13 season, former coach Jose Mourinho's last at the club.
He scored eight goals in 23 La Liga appearances last season.
Even before the injury, he was expected to have a hard time breaking into the Juventus team where Carlos Tevez and Fernando Llorente formed an outstanding partnership in attack last season.
- Sports & Recreation
- Real Madrid
- medial collateral ligament