"Jordi Alba had more tests on Sunday morning to assess the exact extent of the injury he picked up during the first half of the match against Sevilla," Barca said on their website.
"Medical staff confirmed the player sustained a tear in his right hamstring," they added. "The estimated time he will be out of action is approximately three weeks."
Alba, who was replaced by Adriano in the 14th minute of the clash at the Nou Camp, will miss Barca's Champions League Group H games against Ajax and Celtic.
He will also be unavailable for some or all of the champions' La Liga matches against Rayo Vallecano, Real Sociedad, Almeria and Real Valladolid.
The 24-year-old should return in time for Spain's remaining two World Cup Group I qualifiers at home to Belarus and Georgia on Oct. 11 and Oct. 15 respectively.