Jenkins, 22, sustained the injury during the region's European Challenge Cup defeat to Harlequins.
His fellow back-rower Josh Navidi, however, could return for the Pro12 derby at Ospreys on Saturday.
Navidi, who was the Blues' player of the season for the last campaign, has been out of action since October because of a shoulder injury.
Cardiff Blues flanker Ellis Jenkins has been ruled out for six weeks with a knee injury.