Michael Clarke tweaked his right hamstring during the fourth day's play and was forced to retire hurt on 57 after scoring his fastest Test half-century.
He did field in Sri Lanka's second innings, but parked himself at slip to direct the team.
The skipper's setback followed paceman Ben Hilfenhaus's side strain which has prevented him from bowling again in the Hobart Test, though he did bat in Monday's second innings.
Although there is no full diagnosis yet of Clarke's condition, there was speculation that vice-captain Watson could lead Australia in the Boxing Day Test at the Melbourne Cricket Ground, the biggest day on the Australian cricket calendar.
"He's going off for an MRI scan. He's done something to his hamstring and we'll know the extent of that tomorrow," coach Mickey Arthur said.
"He'll get all the treatment he needs. He'll certainly get that tonight and he'll get that tomorrow and between breaks... I think you'll have to cut Michael's leg off from him not to be out there.
"He certainly wants to marshal the troops and I think he certainly wants to be there if hopefully sometime tomorrow we can clinch a win."
Arthur said if Clarke did not recover in time for the second Test, Watson was the obvious contender to lead Australia.
"It is a distinct possibility. I think it will be a really good challenge for Shane," Arthur said.
"We'll learn a lot about Shane and we'll learn a lot about his leadership ability. I'm confident he'll come through that very well."
Arthur, who is also one of five selectors, nominated Brad Haddin, Rob Quiney, Usman Khawaja and Alex Doolan as batting contenders to come into the team for the next Test if Clarke is unavailable.
The coach said a new pace bowler would be needed for the game, with Ben Hilfenhaus ruled out.
Mitchell Johnson, who was left out of the starting eleven for Hobart, is the prime contender to replace him in Melbourne.
Arthur also nominated emerging quicks Jackson Bird or Nathan Coulter-Nile as likely to come into the squad for the next match.