Dozier crumpled to the floor after a collision at the rim during Tuesday night's 119-100 loss to the Portland Trail Blazers, which led to initial fears of a serious injury. Additional tests Wednesday confirmed the tear.
Dozier's loss is yet another blow to a Nuggets lineup beset with injuries. Denver is without Jamal Murray (ACL) and Michael Porter Jr. (lower back) and hopes to have a return soon of MVP Nikola Jokic (wrist). The Nuggets have lost five straight games to drop to 9-9 on the season.
For the Nuggets to be able to apply for hardship waiver help on the roster, they will need to have four players who have missed three games and at least two weeks.
Dozier, 25, has averaged 5.4 points in 18.9 minutes per game this season.
ESPN's Bobby Marks contributed to this report.