Dembele played a full 90 minutes as Barca were beaten 1-0 by Athletic Club on Friday night, Aritz Aduriz scoring an overhead kick in the 89th minute to win it for the hosts.
In the same game Luis Suarez was withdrawn with a calf complaint, while Lionel Messi was unavailable, also with a calf complaint.
Barca have now confirmed the timespan Dembele will be on the sidelines for, revealing in a statement: "A medical examination on Ousmane Dembélé has diagnosed a strain of his left hamstring. The Frenchman is set to be out for approximately five weeks as a result."
This latest news puts an awful lot of responsibility on the shoulders of new signing Antoine Griezmann, who produced an uninspiring performance on his competitive debut for the La Liga champions.
Rafinha was brought on for Suarez after the Uruguayan fell to injury, but how Barca will line up for their first game at Camp Nou this season against Osasuna remains to be seen.
Young midfielder Carles Alena could be pushed into a more attacking role, with Messi still not in full training. The Argentine was expected to be involved on Monday but instead trained on his own, with AS confirming the lack of involvement with his teammates was not down to a setback in his recovery.