The club announced that tests conducted on Monday revealed he suffered a right hamstring injury during the second half of the 4-1 victory against Catalan rivals Girona in the Spanish league on Sunday.
Olmo was substituted in the 61st minute, shortly after scoring the team’s third goal in the match.
The Spain international, who joined from Leipzig this season, has been an essential player for coach Hansi Flick during the team's unbeaten run.
Barcelona has won its first five matches in the Spanish league, currently leading by four points over Atletico Madrid, Real Madrid, and Villarreal.