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.
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."
The absence of Herath, who split the webbing in his bowling hand trying to take a return chance off Jos Buttler in the thumping defeat of England last Sunday, will be more sorely felt on a ground which maintains a reputation for offering something for the spinners.
The International Cricket Council confirmed that Seekkuge Prasanna had been approved as a replacement for Karunaratne, allowing the Sri Lankans the option of fielding a specialist spinner against Australia.
Leg-spinner Prasanna has taken 21 wickets in 22 internationals.
Kusal Janith Perera, a left-handed batsman who has an average of 23.30 from 41 one-day internationals, has also been put on standby to replace Herath if required.
Injury replacements for squad members are allowed at the discretion of tournament organisers the ICC but must be permanent.
Sri Lanka have already lost leg-spinning all-rounder Jeevan Mendis and fast bowler Dhammika Prasad from their original squad for the tournament.
(Reporting by Nick Mulvenney, editing by Patrick Johnston)
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