Umtiti's injury means Barca will have to rely on the injury-prone Thomas Vermaelen to partner Gerard Pique until Javier Mascherano returns from a hamstring problem midway through December.
Vermaelen, who came on to replace Umtiti against Celta, has only started one league game this season.
Umtiti sustained the injury at a crucial stage of the game as he tried to keep up with Celta forward Iago Aspas, who raced towards goal unchallenged to lay on a pass for Maxi Gomez to equalise in the 70th minute.
"Losing Samuel right now is a big loss, he was in excellent form," said Barca coach Ernesto Valverde.
"The injury cost us the goal, it was an accumulation of catastrophes, conceding the equaliser and the injury."
(Reporting by Richard Martin; Editing by Christian Radnedge)
