The news comes as a blow for the 21-year-old, who opened the scoring for the La Liga leaders and has impressed in recent weeks, netting six times in his last 10 outings.
The injury means he is likely to miss both legs of their Copa del Rey quarter-final with Sevilla, and Sunday's Catalan derby at Girona.
It is also possible that he could be sidelined for the visit of Valencia at the beginning of February, although he should be fit for Barca's Champions League last-16 meeting with Olympique Lyonnais in February.
Fellow big-money arrival Philippe Coutinho will be expected to fill the void created by Dembele's absence, with the Brazilian struggling for game time since his 160 million Euros ($181.87 million) move from Liverpool 12 months ago.
(Reporting by Joseph Cassinelli; Editing by Ian Chadband)
