The Brazil international sustained the injury during Saturday's 0-0 draw at Getafe - a match that represented Dani Alves' 200th La Liga appearance for Barca.
Subsequently the full-back underwent treatment on Sunday and he will definitely miss the Copa second leg clash with Huesca at Camp Nou, a tie Barca lead 4-0.
His availability for next weekend's league encounter with Cordoba is also uncertain.
"Dani Alves picked up a hamstring strain in Saturday night's draw against Getafe which will keep him out of Tuesday's cup game against Huesca," read a statement on Barca's official website.
"The Brazilian full-back was given treatment for the injury during training this morning and his availability for next weekend's game remains in doubt."
Dani Alves has made 12 Liga appearances for a Barca side that sit four points adrift of leaders Real Madrid in second.
