The player received a transplant from his cousin Gerard, and expressed gratitude on his Facebook page in a message written by his wife.
"He really wants to thank all of you for your messages, your support, and all the strength you give him. Thanks a Lot!," Hayet Abidal wrote while confirming he had undergone surgery on Tuesday.
The Barcelona defender also received support from his team, which dedicated its 4-0 win against Getafe to the veteran player.
"We know that Abidal and his cousin (Gerard, the donor) are recovering well after the operation," Barcelona president Sandro Rosell said.
The player also received support from many of his teammates during the post-match press conference on Tuesday, as the Catalan team moved within one point of Real Madrid in La Liga.
The transplant took place in relation to a tumor Abidal had removed in March of last year (which resulted in the team dedicating the 2011 UEFA Champions League trophy to him).
There has been no timetable set for his return to the field, but both Rosell and his wife Hayet have confirmed that there have been no complications and his recovery will begin as soon as possible.
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Photo via Flickr/Globovision