Sources have told ESPN the France international will be out for three to five months, although Barca have not given any recovery timeframe.
"Following tests, it's been confirmed he has a dislocation of the biceps tendon in his right knee that will require surgical treatment," Barca said in a short statement on Tuesday.
Dembele has had poor luck with injuries since signing for Barca from Borussia Dortmund for an initial fee of €105 million in 2017.
A hamstring injury ruled him for four months in his first season at the club, while further muscle problems restricted him to just nine appearances in all competitions in 2019-20.
However, the forward remained injury-free last season, playing 44 times and scoring 11 goals under Ronald Koeman.
His performances for Barca earned him a recall to the France squad recently and he came off the bench in both his country's games at Euro 2020 so far, against Germany and Hungary.
This latest setback comes at a time when his long-term future at Barca is unknown.
Dembele's contract expires in 2022 and sources have told ESPN that Barca would have been open to offers for him this summer if he didn't sign an extension.
Barca risk losing him for free next year if he doesn't sign a new deal, but there's unlikely to be any interest now until his knee is fully healed.