Bouye will avoid surgery and should be out just a few weeks, according to Ian Rapoport of NFL Network. The veteran corner will be eligible to return after three weeks under the NFL's new IR rules.
The 29-year-old sustained the injury while attempting to break up a pass during the first half against the Tennessee Titans on Monday.
The club also promoted cornerback De'Vante Bausby to the active roster from its practice squad Wednesday.
Denver acquired Bouye from the Jacksonville Jaguars this past offseason. He has recorded 14 interceptions since entering the NFL in 2013.