A standby player for Clarke has not been named however Marsh said that if he became unavailable, George Bailey would captain the side in his absence.
Clarke, who missed the final three Tests against India following the surgery, has been given until February 21 to prove his fitness for the one-day tournament.
"Captain Michael Clarke will lead our World Cup campaign should he recover from his injury," said chief selector Rod Marsh.
"He is one of the world's best batsmen and we want to give him every chance to prove his fitness for a tournament as important as this one.
"[By February 21] we want to be completely and utterly settled. What we don't want is talk about people's fitness.
"We had to draw the line somewhere; we just couldn't keep it hanging on."
A standby player for Clarke has not been named; however, Marsh said that if he became unavailable, George Bailey would captain the side in his absence.
Clarke, 33, who has a history of chronic back/hamstring trouble, admitted he has a lot of work to do over the next six weeks, but was upbeat he will return as captain.
"I'm confident I'll be fit," said Clarke. "My focus is to get fully fit. However long that takes.”
Darren, Roach get Windies' World Cup nod
Highly-rated off spinner Sunil Narine, top order batsman Darren Bravo and fast-bowler Kemar Roach were all named in the West Indies World Cup squad on late Saturday despite missing out on the current South Africa tour.
Narine was summoned to share spin-bowling duties with Suleiman Benn, Bravo was recalled after choosing to sit out the current series for ‘personal reasons’ while Roach has recovered from an injury suffered in the team's 220-run defeat against South Africa in the first Test last month.
Barbados all-rounder Jason Holder was confirmed as captain with experienced batsman Marlon Samuels appointed vice-captain.
The most experienced ODI player in the squad is opener Chris Gayle with 258 appearances.
"I believe we have selected a very good team which will do West Indies proud at the World Cup," said Clive Lloyd, the West Indies chairman of selectors.
Meanwhile, the UAE also announced it squad with Mohammed Tauqir named as the captain of for the World Cup, replacing Pakistan-born Khurram Khan at the helm.
Squads
Australia: Michael Clarke (capt), George Bailey, Pat Cummins, Xavier Doherty, James Faulkner, Aaron Finch, Brad Haddin, Josh Hazlewood, Mitchell Johnson, Mitchell Marsh, Glenn Maxwell, Steve Smith, Mitchell Starc, David Warner, Shane Watson.
West Indies: Jason Holder (capt), Marlon Samuels, Sulieman Benn, Darren Bravo, Jonathan Carter, Sheldon Cottrell, Chris Gayle, Sunil Narine, Denesh Ramdin, Kemar Roach, Andre Russell, Darren Sammy, Lendl Simmons, Dwayne Smith, Jerome Taylor.
UAE: Mohammed Tauqir (capt), Khurram Khan, Swapnil Patil, Saqlain Haider, Amjad Javed, Shaiman Anwar, Amjad Ali, Nasir Aziz, Rohan Mustafa, Manjula Guruge, Andri Berenger, Fahad Al Hashmi, Muhammad Naveed, Kamran Shahzad, Krishna Karate.
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