The France global was injured in the 24th minute against Getafe and was forced to leave the field.
Barca revealed during the game that Dembele had suffered a hamstring problem and he has now flown to Finland for an operation.
"Ousmane Dembele has ruptured the tendon in his femoral bicep in his left thigh".
"Dembele? It looks like a muscle tear and it's a shame because he was getting into the team's dynamics and now it'll have to stop, hopefully not for long", Valverde told reporters.More news: Sean Spicer: Being invited to the Emmys was 'a real honor'
The Catalan giants signed 20-year-old Dembele from Borussia Dortmund in a deal worth up to £135.5 million in August to replace Neymar after the Brazilian left for Paris Saint-Germain. The player will be operated on by Dr. Sakari Orava in Finland this week. "Following the surgery, the club will provide a medical statement".
Gerard Deulofeu, who may profit from Dembele's injury, said: "It is a good three points because it was a field that couldn't be played on".
If he is to sit out the next four months, then he will not come back into contention until mid-January.
It was his first La Liga start for the Spanish club following substitute appearances against Juventus and Espanyol.