Alves had to be replaced by Sergi Roberto after 19 minutes at San Mames after clashing with Bilbao striker Aritz Aduriz, while Busquets was taken off on a stretcher in the second half after tangling with the same player, with Marc Bartra coming on.
Barca did not say how long Brazil international Alves might be sidelined, though Spanish media reported he could be out for a month.
"In contrast, tests on Sergio Busquets showed the midfielder suffered a slight ankle injury but nothing significant," Barca said on their website (www.fcbarcelona.es).
Barcelona host Malaga on Saturday for their second game of the La Liga campaign before a trip to 2014 champions Atletico Madrid on Sept. 12.
Luis Enrique's side, who won the treble last season, are chasing a sixth Spanish league title in eight years.
(This story corrects date of Atletico match in penultimate paragraph)
(Reporting by Iain Rogers, editing by Ken Ferris)
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