Clarke, 31, sprained his right ankle during a fielding drill at Australia training on Tuesday morning.
The in-form skipper was whisked away for scans, but despite X-rays clearing Clarke of any damage to his ankle, he will not appear in the fifth and final ODI against the Lankans.
He will be replaced as captain by George Bailey.
Clarke now has two weeks to rest and recover ahead of taking back the captaincy reins for the start of a five-match limited-over series against the West Indies, starting in Perth on Friday, February 1.
Australia must win Wednesday night's match without their skipper and number one batsman, to tie the series at 2-2, after the fourth clash in Sydney was abandoned on Sunday due to rain.
The loss of Clarke is a significant blow to Australia's fragile top-order, which has been prone to collapse during the fifty-overs series against Sri Lanka.
The tourists lead the series 2-1.