Schefter added the Cardinals are handling the injury "like a high ankle sprain."
Chase Edmonds took over and will presumably see an expanded role going forward after impressing in limited playing time this year. Jonathan Ward and Eno Benjamin are the only other running backs on the roster.
The Cardinals offense could suffer without Drake, who has been productive in his first full season with the team.
The 26-year-old has recorded 512 rushing yards and four touchdowns in seven games, averaging 4.3 yards per carry. He had a breakout 2019 when he rushed for 643 yards with eight scores in eight games for Arizona after a midseason trade from the Miami Dolphins.
Arizona placed the transition tag on Drake this past offseason, and he has rewarded the team with solid play, including a big showing of 164 rushing yards and two scores in a win against the Dallas Cowboys in Week 6. Despite some inconsistency, the running back is third in the league in rushing yards.
Drake is set to enter free agency this offseason, so he will hope this injury doesn't linger and hinder his ability to perform for a considerable amount of time.