The attacking midfielder, who also damaged his meniscus, will undergo surgery Monday.
The injury almost certainly means the Italian international will miss Euro 2020 this summer, though Roma are expected to provide an official timeline for his recovery after the operation is completed.
Zaniolo, who was in tears before being stretchered off at the Olimpico, was hurt during an awkward collision involving Adrien Rabiot and Matthijs de Ligt. The incident came after the Roma youngster had gone on a mesmerizing solo run to the edge of the Juventus penalty area.
The versatile attacking midfielder burst onto the scene last season with his combination of trickery and powerful dribbling, and has recorded four Serie A goals during the 2019-20 campaign.