Dembele had to be withdrawn in the first half of his side's dramatic 2-1 victory on Saturday, leaving the field after sustaining the problem while attempting a back-heel near the corner flag when the match was still goalless.
Barca confirmed during the game that the 20-year-old had suffered the problem in his left hamstring during what was his full La Liga debut and would undergo tests to determine the severity of his injury.
And Valverde fears it is a muscle tear, although he will wait until he has a definite diagnosis before speculating over how long Dembele will be out.
"He is going to have to spend some time on the sidelines," Valverde told reporters after the match.
"It is a muscle problem. We think it is a tear, but we will do more tests on Sunday.
"It is a shame because he was just getting up to scratch with the team's dynamic. We hope he won't be out for a long time."
Barca, who have won all four of their La Liga matches to start the new season, have clashes against Eibar, Girona, Sporting CP and Las Palmas before the next international break, after which they are away to Atletico Madrid on October 14.
Signed for an initial €105 million, ex-Borussia Dortmund winger Dembele had made his first Barca start against Juventus in the Champions League on Tuesday, having come on as a substitute at home to Espanyol last week, his first game in the club's colours.