Surgeons discovered the tendon was fully torn off the bone at the shoulder joint and used a screw to reattach it.
Symonds tore the muscle during Friday's shock loss to England and his probable absence from the West Indies tournament is a massive blow to Australia's planning as they aim for an unprecedented third straight World Cup victory.
He has already been ruled out of the rest of the tri-series tournament, also involving New Zealand, and the subsequent Chappell-Hadlee Trophy matches in New Zealand.
Australia's physiotherapist Alex Kountouris admitted Symonds was only an outside chance for the World Cup.
"It's going to be tough for the World Cup," Kountouris said in Melbourne on Sunday.
"The surgery went well, but they found a fair bit of damage. His tendon was actually a bit worse than we expected.
"We are not really looking at the World Cup right now -- we can't say if he will be right in four or five or six weeks. We are just looking at it week by week."
It was the support of skipper Ricky Ponting that earned Symonds a surprise berth at the 2003 World Cup, in which he surpassed most expectations to arrive as one of the most damaging players in one-day cricket.
Speaking before Sunday's clash with New Zealand at the MCG, in Melbourne, Ponting said he wanted to see Symonds in the 15-man squad for the Caribbean.
"He's torn a tendon in his shoulder and had surgery early this morning," Ponting said.
"Hopefully, his recovery goes as well as expected and we can get him back at some stage during the World Cup."
Australia's first World Cup game is against minnows Scotland on March 14 and with the Super Eights stage not starting until March 27, there could be a temptation to carry Symonds through the early stages of the tournament in the hope he will be fit for the knockout stages.
Symonds, with his bludgeoning batting, brilliant fielding and ability to bowl both spin and medium pace, was a pivotal part of Australia's plans and his likely absence will force a major rethink.
If he is missing, star batsman Mike Hussey could be promoted to No.5, something the Australians have been reluctant to do.
Queensland all-rounder Shane Watson has resumed playing at domestic level after his recurring hamstring problems earlier in the summer and could slot into the middle order and also offer an extra bowling option.
The national selectors will certainly be paying great attention to Watson's fitness after Friday's developments and provided he does not break down again, he looks certain to be part of the squad.
However, he does not offer the same power hitting as Symonds towards the end of games.
If the Australians do not have the option of Symonds' spin, there will be extra pressure on likely squad members Cameron White and Brad Hogg, who has played just once in the tri-series, to perform in that role.
White will also need to find improved form with the bat, as he is a player capable of providing the big shots late in an innings.
Victorian batsman Brad Hodge is also in contention for the World Cup, while Western Australia batsman Adam Voges may be an outside chance, as he can bowl useful finger spinners and was in the third Test squad earlier in the season.
Queensland all-rounder James Hopes will be another in the mix should Symonds be ruled out.