Finalists at the last two World Cups, the Sri Lankans are second in Pool A behind New Zealand heading into Sunday's crunch match at the Sydney Cricket Ground against Australia.
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They will have to take on the co-hosts without left-handed batsman Karunaratne and left-arm spinner Herath, however.
"Dimuth is unfortunate, he fractured his finger in fielding practice yesterday so he's been declared unfit, he probably needs an operation," Jayawardene told reporters at the ground.
"I'm not sure how bad or long it will take but he's definitely going back home.
"With Rangana, he's had stitches in his fingers so we need to give him five or six days for him to heal properly then the stitches will come off then we'll see how he progresses."
Kusal Janith Perera, another left-handed batsman who has an average of 23.30 from 41 one-day internationals, has been put on standby to replace Karunaratne.
Seekkuge Prasanna has also been summoned as precautionary cover for Herath, who split the webbing in hisbowling hand trying to take a return chance off Jos Buttler in the thumping defeat of England last Sunday.
Herath's absence from the match against Australia will be more sorely felt on a ground which maintains a reputation for offering something for the spinners.
Injury replacements for squad members are allowed at the discretion of tournament organisers but must be permanent.
ESPN Cricinfo reported that Prasanna would now be a formally nominated as a replacement for Karunaratne, allowing the Sri Lankans to field a specialist spinner against Australia.
Sri Lanka have already lost leg-spinning all-rounder Jeevan Mendis and fast bowler Dhammika Prasad from their original squad for the tournament.
Image: Dimuth Karunaratne
Photograph: Dinuka Liyanawatte/Files/Reuters
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