The 33-year-old has suffered persistent hamstring trouble in the last year and was ruled out of the recent Test series with India to have more surgery.
After his latest injury setback, he admitted his career could be in doubt.
National selector Rod Marsh said Clarke would be replaced if he was not fit by Australia's second World Cup match, against Bangladesh on 21 February.
Clarke, who made his international debut in 2003, is not expected to feature in the preceding one-day tri-series against England and India which begins on 16 January.
The Australians begin their World Cup campaign against England in Melbourne on 14 February, and play Bangladesh a week later.
"We have said that if Michael has not recovered by our second match of the tournament against Bangladesh on 21 February, we will replace him in the squad," said Marsh. "He understands that and is working tirelessly with medical staff to get back to fitness.
"Our medical staff are pleased with his progress and he continues to undergo thorough rehabilitation work with a view to being ready to play an important role in the World Cup."
A stand-by for Clarke has not been announced, although Marsh said that if the captain became unavailable, regular deputy George Bailey would lead the side in his absence.
Marsh also said Western Australia all-rounder Mitchell Marsh is on track to be fit for the start of the World Cup.
"Mitchell is progressing well with his rehab and we expect him to be available at some stage during the tri-series with the aim to have him well prepared for the World Cup," he said.
Elsewhere in the squad, Brad Haddin is preferred to Matthew Wade as wicketkeeper, while Nathan Lyon misses out in favour of Xavier Doherty for the solitary spinner's slot.
Lyon has played just eight one-day internationals, but made a late push for selection with 23 wickets in four Tests against India.
Australia are seeking a record fifth World Cup after winning the tournament in India in 1987, England in 1999, South Africa in 2003 and the West Indies in 2007.
Australia World Cup squad: Michael Clarke (capt), George Bailey (vice-capt), Patrick Cummins, Xavier Doherty, James Faulkner, Aaron Finch, Brad Haddin (wk), Josh Hazlewood, Mitchell Johnson, Mitchell Marsh, Glenn Maxwell, Steve Smith, Mitchell Starc, David Warner, Shane Watson.
Click here for a list of all the World Cup squads
Michael Clarke has been declared fit to captain co-hosts Australia at the World Cup which begins next month.