The Spain international was carried off in the eighth minute of Sunday's game following a challenge from Eibar's Nicolas Escalante.
"Results on Monday confirm that Busquets has a sprained external lateral ligament in his right ankle," Barca said in a statement.
"The player is out and his return will depend on his recovery."
Barcelona face Paris St Germain on Feb. 14 in the first leg of their Champions League last 16 tie and will hope to have the 28-year-old available.
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Busquets has played 27 of Barcelona's 32 games in all competitions this season.
Barca, third in La Liga and two points adrift of league leaders Real Madrid, who have a game in hand, host Real Sociedad on Thursday in the King's Cup quarter-final second leg holding a 1-0 advantage.
(Reporting by Adriana Garcia, editing by Ed Osmond)
