The France international was replaced by Luis Suarez at half-time of Saturday's 1-0 victory away to Real Valladolid.
Medical tests on Sunday showed Griezmann has damaged the quadriceps in his right leg and is facing a spell out of action.
The 2018 World Cup winner, a €120million signing from Atletico Madrid last year, is likely to miss Thursday's league match against Osasuna at Camp Nou.
❗[LATEST NEWS] Tests this morning have shown that Antoine Griezmann has a quadriceps muscle injury in his right leg. He is not available for selection and the evolution of the injury will condition his availability.https://t.co/G7caKZS9Io pic.twitter.com/7jxrypVRsj— FC Barcelona (@FCBarcelona) July 12, 2020
Griezmann has scored just nine goals in 35 league appearances during a difficult first season with Barca.
He was dropped from the starting line-up by coach Quique Setien for the 2-2 draws with Celta Vigo and Atleti last month but made a goalscoring return in the 4-1 win over Villarreal on July 5.