Ponting sustained the injury during the third ODI of the five-match series, that Australia clinched 5-0 on Sunday.
"Ricky has sustained a tendon injury that requires repair of tissues that hold the tendon in place. This surgery was
performed today," Cricket Australia Medical Officer Trefor
James said.
Ponting was also reviewed by CA's medical staff in consultation with a wrist specialist.
"Ponting's recovery will be monitored in the coming weeks and a decision regarding his fitness for the upcoming series against Bangladesh and then the Champions Trophy will be made in due course," CA said in a statement.