Bernal sustained the injury to his left knee during Tuesday's 2-1 victory at Rayo Vallecano, where he was forced off the pitch in the final minutes.
Bernal, who made his debut in Barca's opening-day win over Valencia, also suffered an associated injury to the external meniscus. "He will undergo surgical treatment in the coming days," Barcelona said in a statement.
Barcelona face Real Valladolid next in LaLiga on Saturday.