Brazil international Neymar damaged the fourth metatarsal in his left foot during Wednesday's Copa del Rey final defeat to Real Madrid, while left-back Alba injured his right hamstring in the same match and was subsequently replaced by Adriano at half-time.
A statement on Barca's website said: "Neymar Jr. ended the Copa del Rey final against Real Madrid injured. The player suffered a concussion that caused edema in the fourth metatarsal in his left foot.
"It is expected that the Barca No.11 will start with specific treatment and his downtime is approximately four weeks.
"If deadlines are met Neymar recovery could participate in the last game of the season; May 18 when the Catalans will play at the Camp Nou against Atletico Madrid."
The 2-1 Copa loss saw another trophy slip from Barca's reach, having exited the UEFA Champions League at the hands of Atletico Madrid last week, before falling four points behind Diego Simeone's men in the Liga title race thanks to a 1-0 defeat to Granada.
Neymar has scored nine league goals and added a further nine assists in his debut season in Spain, but he has disappointed some in recent weeks, with calls for coach Gerardo Martino to replace him with Alexis Sanchez or Pedro.
Alba is, like Neymar, set for four weeks out, and Barca confirmed that Marc Bartra – their goalscorer on Wednesday – also suffered a hamstring strain, but he should be fit for this weekend's game against Athletic Bilbao.
Thursday's statement added: "The club's medical services have confirmed that Jordi Alba suffered a hamstring injury in the femoral biceps of his right leg and will be sidelined three to four weeks.
"Marc Bartra has not been able to exercise either due to overloading the hamstrings of the right leg. The scorer of the Catalan goal in the final has commenced specific work and his progress marked the availability for Sunday's game against Athletic Club."
