The lingering injury, sustained in the Champions League quarter-final first leg at Paris St Germain on April 2, has kept the World Player of the Year out of several key games and he was forced off on Sunday during a league match at Atletico Madrid.
"The period of absence will be two to three weeks," Barca said on their website.
Messi is likely to miss Barca's remaining three La Liga matches, including Sunday's game at home to Real Valladolid - the club's first at their Nou Camp stadium since they wrapped up a fourth title in five years at the weekend.
The 25-year-old will also miss out on a chance to equal or break his record for league goals of 50 set last season. He currently has 46 from 32 appearances.
However, he should be fit for Argentina's World Cup qualifiers at home to Colombia on June 7 and away to Ecuador four days later.
Argentina top South American qualification with 24 points from 11 matches. Ecuador are second on 20 and Colombia third on 19 with both having played one game fewer.