Barca were beaten 2-0 on Saturday night after making multiple changes, with Lionel Messi, Luis Suarez, Philippe Coutinho and Ivan Rakitic all playing no part.
Dembele was handed a rare start alongside Malcom and Kevin-Prince Boateng, but his day was ruined when he suffered an injury three minutes into the game.
He was brought off for 20-year-old Alex Collado, who was making his first league start for Barca.
Speaking after the defeat, Valverde admitted that losing Dembele was a “major blow” to his side.
“With Dembele, it looks like a tear,” he said. “We had already noticed during the play that something was not right.
“We were worried quickly because it seems like a muscular tear.
“It is certainly not muscle fatigue because the other day he played very little [in the Champions League win over Liverpool on Wednesday].
“These things happen and as a coach I do not have an explanation.
“He is an important player for us and it is a major blow with the big games we have coming up.
“I didn’t replace him with Philippe Coutinho as I didn’t want to run any more risks.”
Barcelona’s league campaign is already over, as they secured the league title last weekend, however they have a treble to aim for.
With the league already won, and a Copa del Rey final to prepare for against Valencia, Valverde’s focus will no doubt be on Tuesday night’s Champions League semi-final against Liverpool.
Barca will head to Anfield with a 3-0 lead after an impressive performance at the Nou Camp.
Lionel Messi’s double and Luis Suarez’ early goal earned the Catalan giants the advantage headed back to the Nou Camp.
And they will no doubt have been aided by the fact that they could rest players on Saturday night, whereas Liverpool – who are in a fierce battle with Manchester City for the Premier League title – had to play a full strength team against Newcastle.
And they were dealt an injury issue of their own, as Mohamed Salah was stretchered off in the second half with a head injury.
Jurgen Klopp also confirmed that Roberto Firmino will also be unavailable for selection.