Brazil international Neymar has a bruise on his left foot which has caused a build-up of fluid while Spain left back Alba has a strain in his right thigh, Barca said on their website (www.fcbarcelona.es).
The injuries were sustained during Wednesday's Copa del Rey final defeat to Real Madrid, with Neymar sidelined for about four weeks and Alba for three to four weeks, leaving them in a race to regain fitness before the end of the season.
If they recover within the estimated timeframe, they should return for Barca's final Liga match at home to current league leaders Atletico Madrid on May 18, the club added.
The Catalan side's 2-1 defeat by Real in the Copa showpiece followed their Champions League exit at the hands of Atletico a week earlier and a shock 1-0 La Liga defeat at Granada last weekend.
With five games left, Barca are third in the standings, four points behind Atletico and one behind second-placed Real.
Centre back Marc Bartra tweaked a hamstring in the Cup final and is a doubt for Sunday's league game at home to fourth-placed Athletic Bilbao.
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