The full-back was injured in the 2-2 draw with Real Madrid at the Camp Nou and is likely to miss games against Deportivo La Coruna and Rayo Vallecano.
The Brazilian will also miss upcoming friendlies against Iraq and Japan on October 11 and 16 respectively.
A statement on Barcelona’s official website said:
“Dani Alves will be out of action for three weeks. The Brazilian picked up a hamstring injury in his left leg in the match against Real Madrid. Martín Montoya came on in his stead on the 27th minute.”
Two goals each from Cristiano Ronaldo and Lionel Messi ensured that the spoils were shared in El Clasico while Barcelona maintained their eight-point advantage over their fiercest rivals.