The young Spanish forward sealed his €20 million (£15.8m) move to the Serie A champions on Saturday from Real Madrid, only to suffer the setback on Monday.
The 21-year-old limped from the training pitch complaining of pain in his knee and is now awaiting the results of further tests to determine the extent of the damage.
"During training this afternoon Alvaro Morata has reported a sprain in his left knee," Juventus confirmed on their official website. "His condition will be evaluated tomorrow."
Morata will be hoping to receive the all clear from the medical staff as he looks to settle quickly at Juve and fight Carlos Tevez and Fernando Llorente for a regular starting spot under Massimiliano Allegri.
Juve's new coach replaced Antonio Conte on Wednesday and made Morata his first signing as he looks to continue the period of success that has brought three-consecutive Scudetti.
A lack of regular first-team football hampered his progress in Madrid, though he was thought of highly enough for Real to retain an option to buy him back until the end of the 2016-17 season.