Clarke re-injured his problematic left hamstring in Australia's 23-run win over the Proteas in Perth on Friday and will further consult with specialists after having scans on Saturday.
The 33-year-old's injury sidelined him for the entire one-day series against Pakistan in the United Arab Emirates and almost all of a preceding one-day tournament against South Africa and hosts Zimbabwe.
The recurrence of the injury has stoked fears Australia could head into a four-test series against India without their top batsman and master tactician, while another breakdown could be the end of his World Cup ambitions.
Australia coach Darren Lehmann confirmed Clarke would miss the second ODI match in Perth on Sunday and would be replaced by middle order batsman Steven Smith.
Bailey, who led the team after Clarke was ruled out midway through the match after being caught behind for 11, will continue to captain.
Lehmann said Australia could win the World Cup with or without Clarke.
"It's never easy when you're losing one of your best players, but that's part and parcel of sport these days," Lehmann told reporters in Perth on Saturday.
"Players have got to be adaptable.
"We'd love him there. But you can (still) win every game you play (without him).
"With the 11 that go on the field, we have full faith in winning each and every game."
With ever injury breakdown, Australian media have called on Clarke to step down as ODI captain to prolong his career in tests, considered by far the most important format in Australia.
Pundits repeated the calls in newspapers on Saturday.
Lehmann said it would be Clarke's call as to whether he continued in the role.