The US international missed the final match of the pre-season tour of his homeland which Juve lost 2-0 to Real Madrid.
And Gazzetta dello Sport among other report he will be out for a month after dislocating his shoulder.
The news will come as a huge blow to coach Massimiliano Allegri, who is already without new signing Paul Pogba.
The France midfielder will reportedly decide on Monday whether to undergo a knee operation which could potentially cost him a place at the World Cup later this year and keep him out of action until 2023.
McKennie joined Juve initially in a loan deal in 2020 before the move became permanent six months later.
During his two seasons with the club, he has made 44 appearances and scored five goals.