Clarke remains in doubt for Australia's tournament opener against England Feb 14 but the skipper's bid to return from a hamstring injury in time for the second match was given a major boost Saturday when he scored 51 for club side Western Suburbs.
"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."
When the World Cup squad was announced last month, national selector Rod Marsh said Clarke would be given until Australia's second match of the tournament against Bangladesh Feb 21 to prove his fitness.
But Warne said Clarke should play the first game if possible, adding that once Clarke returned, he expected fill-in skipper George Bailey to drop out of the starting eleven.
"We all admire Clarke's imagination and flair as a captain so I would get him in for that first game if he proves his fitness," he said.
"Good bowlers can bowl at (stand-in skipper) 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 he believed ODI tri-Series man of the series, pacer Mitchell Starc had now cemented his spot in Australia's World Cup line-up. A development which meant Australia could potentially field three left-armers.
"Starc will be key. He has really played well in the one-dayers, making the white ball talk, and his death bowling is pretty good," added Warne.
"I don't think Australia would like to play three left-armers in (James) Faulkner, Starc and (Mitchell) Johnson but with their form at the moment they may have to."
Like many, Warne has tipped Australia to win the World Cup.
"I can't really think of too many weaknesses in Australia side," said Warne, who was part of the victorious 1999 Australian team.