Tests following his injury during Wednesday's 1-0 win over Celta Vigo confirmed the diagnosis. Yamal scored the winning penalty before collapsing on the pitch, grabbing his left hamstring.
Head coach Hansi Flick said afterwards: "We have to wait. He felt it. After the goal, he would not leave the pitch without reason. So it is something."
Spanish football website AS reports the expected recovery window is four to five weeks, which means he should be available for the World Cup if he avoids any setback. Spain face Cape Verde in their opening group game on 15 June.
However, hamstring injuries in explosive players carry a known relapse risk, and the club's medical staff will exercise the maximum caution. Raphinha suffered a recurrence during a similar recovery this season, adding two weeks to his lay-off.
Yamal's absence covers six remaining LaLiga fixtures, including the final ClĂĄsico against Real Madrid on 10 May. Barcelona lead the league by nine points and remain well-positioned to win the title without him.
Flick is expected to receive Marc Bernal and Raphinha back in the coming days to provide attacking cover.
Yamal has scored 16 goals and provided 11 assists in LaLiga this season, as well as six goals and four assists in the Champions League.