"The player was released from hospital last night and is resting at home," Barca said on their website.
"The post-operation procedures were satisfactory in every aspect and there were no complications," the club added.
Abidal will continue his recovery at home and should be able to begin physical exercise again in four weeks with a view to resuming training.
The 31-year-old, who has been in superb form this season, joined Barca from Olympique Lyon in 2007 and has also played for Ligue 1 sides Lille and AS Monaco.
He has made 52 appearances for France, including the 2006 World Cup Final against Italy when he scored a penalty in the shootout which the Italians won 5-3.
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