The Wales flanker, who will join up with the rest of the squad in Queensland on Monday, was assisted from the field after 68 minutes of the 16-15 defeat to the Wallabies on Saturday night which levelled up the series at 1-1.
Warburton gave his best performance of the tour to date in Melbourne to help the Lions win the battle of the breakdown and it was only after he left the field that Australia scored what turned out to be the winning try.
"Coming off in a Test match like that is devastating," assistant coach Andy Farrell told reporters in Queensland on Sunday.
"As a captain, you want to be there for your troops and lead from the front, especially in the dying minutes of the game.
"He's disappointed with that, but he's in good spirits because we have a big week ahead of us with a Test match to win. He's gone for a scan and will find out the results later."
The rest of the Lions party flew to Noosa on Queensland's Sunshine Coast for rest and recuperation on Sunday and will not return to Sydney for Saturday's decider at the Olympic Stadium until Thursday afternoon.
Farrell said the injury to Warburton was the only one suffered by the Lions in Melbourne and that the players already on the injury list, prop Alex Corbisiero (calf) and Jamie Roberts (hamstring), would return to training on Wednesday.
Warburton, who was rested from the first two tour matches because of a sore knee, said after Saturday's match that the injury was a new one for him.
"I have a sore hamstring. The normal protocol is to ice it every two hours and then assess it after 24 hours. I haven't done it before - this is a new injury," he told reporters.
"I will do anything I can to play in that because if we win next weekend it will be in more dramatic fashion than it would have been this week."
Lions coach Warren Gatland described his captain's performance at the breakdown at the Docklands Stadium as "brilliant".
"We've had a number of turnovers and I think that was the difference in the two sides," he said.
The Lions do have plenty of options should Warburton prove unfit to play in Sydney with Ireland's Sean O'Brien able to play both openside and blindside, while Justin Tipuric has been in brilliant form for Wales this year.
Australia coach Robbie Deans, who could yet lose his skipper James Horwill to a stamping charge, said he also thought Warburton had played an excellent game in Melbourne.
"He played well, he played very well," the New Zealander said in Melbourne on Sunday.
"Obviously Sam would rather be there than not, he's captain. It would be a tough pill for him to swallow if he's not able to start the game.
"But they've got some able replacements as well. Whoever turns out is going to be a good player."
Farrell said the Lions would spend the next couple of days "licking their wounds" before getting down to the business of preparing for the Sydney Test.
"We all realise it's the biggest game of our lives," he said.
"I wouldn't say Australia are in the driving seat. I'd say they're very pleased, it was a do or die situation for them and they rose to the challenge.
"It was a one-point game that could have gone either way and both teams will be confident about next week."
Scrum-half Mike Phillips is also hoping to be involved after missing Saturday's defeat due to a knee injury.
The Welshman admitted he was hugely disappointed to have been left out by the Lions coaches despite having made good strides in his recovery.
"When Rob Howley told me I hadn't been selected for the second Test it was absolutely devastating news," he told the Mail on Sunday.
"My heart sank and I had a weird feeling in my stomach. It was incredibly hard to watch from the stands on Saturday, especially after being involved last week.
"Rob said the coaches had taken the decision to rest me from Saturday's game because of my knee, but I'm a proud man and I still felt I could have done a job for the team."
- Sports & Recreation
- Andy Farrell