Clarke scored 51 on his comeback match in Sydney club cricket on Saturday after undergoing surgery on his hamstring in December.
The 31-year-old skipper was injured during the first Test against India in Adelaide and Steve Smith and George Bailey took over the captaincy duties in Tests and ODIs respectively.
"I don't think Australia can win the World Cup without Clarke," Warne told Sky Sports.
"Australia were in disarray just over 12 months ago but under his captaincy, they won the Ashes 5-0 and then beat South Africa in South Africa.
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Bailey captained Australia clinched the ODI tri-series title after defeating England by 112 runs in the final in Perth yesterday.
However, Warne said if Clarke is fit then Bailey will not figure in his playing XI as the stand-in skipper is not a strong enough batsman.
"Good bowlers can bowl at George Bailey and make him unable to hurt you, so I would say if Clarke is fit he drops out, as the rest of the top five - David Warner, Aaron Finch, Shane Watson and Steve Smith - picks itself," Warne said.
Australia won the World Cup in 1987, 1999, 2003 and 2007.