Ponting, who left the Caribbean with two one-day internationals to play against the West Indies to seek treatment, had an assessment with Cricket Australia medical officer Trefor James and wrist specialist Greg Hoy.
He then had surgery to repair the tissues that hold a tendon in place in his right wrist, which he injured in the third one-day international against the West Indies in Grenada last week, CA said.
Ponting had the surgery to give him extra recovery time ahead of Australia's three one-dayers against Bangladesh in Darwin next month and September.
The Bangladesh series will serve as a warm-up to the Champions Trophy tournament in Pakistan.
"We're not sure at this stage," a CA spokesman said of the skipper's availability for the Darwin series.
"We'll have to assess him as we go along. But that's why they got him in for assessment so quickly, so they could decide on a course of action rather than him leaving it for a week. This way it gives him more time to recover."
Michael Clarke captained the one-day side for the first time in Ponting's absence, leading them to a 5-0 series whitewash of the West Indies in St Kitts on Sunday.
Australia is expected to name a provisional 30-player squad for the Champions Trophy later this week.