The France international entered the operating room at the Barna Clinic at 10.00CET for the essential medical procedure, which is expected to last approximately eight hours.
It emerged in March that Abidal needed a transplant just a year after having a tumour removed from his liver.
The versatile full-back's cousin stepped forward to act as a donor for the surgery, which is being carried out by Dr. Juan Garcia Valdecasas.
Barca will issue an update on Abidal's condition once the operation has been completed.
Abidal, who has continued training with the Blaugrana in recent weeks, made a rapid recovery from his first surgery, returning in time to play his part in their Champions League victory over Manchester United at Wembley in May.
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