The Celtic striker sustained the injury during the 2-0 win over Rangers in the semi-final at Hampden on Sunday.
The Parkhead side’s top-scorer limped off after just half an hour.
Dembele underwent a scan to assess the extent of the damage.
With the Scottish Cup final against Aberdeen taking place on 27 May he is unlikely to be risked, particularly with Celtic’s first Champions League qualifiers for next season scheduled for 11-12 July.
Dembele’s injury is likely to open the door to Leigh Griffiths to take the lead striker’s role as Celtic seek to complete a domestic treble for the first time since 2001.
Griffths was the club’s top scorer last season but has found his chances limited during this campaign due to Dembele’s excellent form.