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.