Muralitharan, who has so far claimed 532 Test scalps in 91 matches, was successfully operated on his bowling shoulder on Monday night at Melbourne and would need at least five months' rest to recover, Australian Broadcasting Corporation (ABC) reported in Sydney on Tuesday.
The ace off-spinner claimed five wickets in the first Test against South Africa last month to take a sole lead in the wicket takers list but had to opt out of the second Test complaining of shoulder pain.
With Muralitharan under rehabilitation, Australian leg-spinner Shane Warne, with 527 wickets, will have a great chance to regain the top spot, which he held jointly for a brief period with his Lankan rival.
Dr Jerome Young, who operated on the bowler, said there was a lesion on the bowler's shoulder that was causing problems.
"I thought there would be a fair bit of wear and tear on the shoulder. We didn't find that, we found a lesion and that in turn was pressing on a nerve and starting to weaken the muscle and that was our real concern," he was quoted as saying by ABC.
The 32-year-old bowler will stay in Melbourne for the next two weeks for observation before returning to Sri Lanka.