Skipper Steve Smith said the opener, who suffered the quad injury while fielding but struggled on to scored 20 runs from 15 balls before the game was washed out, is unlikely to be fit to face India or New Zealand on Tuesday or Wednesday.
Sri Lanka are still 518 runs behind and will need a Herculean effort to avoid the follow-on even though more rain is forecast for Saturday.
This is Sri Lanka's biggest victory over Australia in ODIs in terms of runs.
Australia's middle order enforcer Josh Inglis said their depleted side will draw a lot of confidence after pulling off a record chase against England in their Champions Trophy opener on Saturday.
Spin twins Matthew Kuhnemann and Nathan Lyon combined to dismantle Sri Lanka and bowl Australia to a crushing victory by an innings and 242 runs in the opening Test in Galle on Saturday.
Smith's unbeaten 120 is his second successive hundred of the series while Carey made a career-best 139 not out hitting 22 fours and three sixes between them.
Sri Lanka captain Charith Asalanka led by example and smashed a belligerent hundred to set up a 49-run victory over a depleted Australia.
With India's pacer spearhead not there to open the bowling on Sunday, the pace duo of Mohammed Siraj and Prasidh Krishna were all over the place, leaking 35 runs in the first three overs.
Australia bowled out Sri Lanka for 231 in the hosts' second innings and then chased down the target of 75 losing the lone wicket of opener Travis Head.
England had moved to within 35 runs of securing a famous victory over India when bad light and torrential rain ended an extraordinary fourth day of the final Test at The Oval on Sunday.
Australia's Usman Khawaja struck a maiden double hundred and Josh Inglis got a century on his Test debut against Sri Lanka to power the tourists to a mammoth 654/6.
Siraj now has 203 international wickets in 101 matches, surpassing Sachin Tendulkar, who had 201 wickets in his career.
They will meet the winner of Wednesday's second semi-final between South Africa and New Zealand in the final in Dubai on Sunday.
Images from the ICC Champions League Group B match between Afghanistan and Australia in Lahore, on Friday.
Nitish Kumar Reddy made a promise to himself post the Australia tour that he would improve his bowling.
England skipper Jos Buttler expressed delight in Ben Duckett's record-breaking knock even as he hailed Australia for chasing down a massive total of 352 runs in the ICC Champions Trophy Group B match in Lahore on Saturday.
England vice-captain Ollie Pope won't be surprised if Joe Root overtakes Sachin Tendulkar and becomes the all-time leading run-getter in Tests.
'I didn't know that we'd won kind of everything until half an hour ago but that's always the aim.'
Injured wicketkeeper-batter Rishabh Pant will bat on day five of the fourth Test, said India batting coach Sitanshu Kotak on Saturday.
Steve Smith became the 15th member of Test cricket's 10,000-run club as he and opener Usman Khawaja smashed hundreds to help Australia rack up 330/2 on the opening day of the first Test against Sri Lanka.
A South African side missing several regulars will resume on 49 for one on the third morning after Zimbabwe made 251 in reply to the tourists' first-innings score of 418 for nine declared.
Australia's stand-in captain Steve Smith hailed his side's resounding innings and 242-run victory over Sri Lanka in Galle on Saturday as "near flawless" after the visitors retained the Warne-Muralitharan Trophy.
Jasprit Bumrah takes a fifer at Lord's and goes past Kapil Dev for most five wicket hauls in away Tests.
Yashasvi Jaiswal wanted to be more consistent on his first tour of England but drew immense satisfaction from his second-innings ton on a "spicy" pitch at The Oval to help India set a massive 374-run target in the fifth Test.
IMAGES from Day 1 of the WTC Final between Australia and South Africa at Lord's on Wednesday
A dominant Australia hammered India by 10 wickets in the day-night second Test on Sunday to level the five-match series 1-1.
He has taken nine five-wicket hauls in SENA conditions.
Dimuth Karunaratne's Test career ended in a whimper as Sri Lanka's most prolific Test opener fell caught behind to Kuhnemann after making 14.
India are favourites to secure victory and draw the series, but England will still fancy their chances of completing what would be by far the highest successful Test run chase at The Oval.
'...there was a time there where it could have been 250 or 270 (run lead) or maybe even less there for a bit.'
Australia took the upper hand in the World Test Championship final against South Africa at Lord's, ending day two on 144-8 in their second innings with a lead of 218 runs after wickets tumbled freely again on Thursday.
Daniel Vettori admitted that a resilient partnership between Indian tailenders Jasprit Bumrah and Akash Deep foiled their plans to enforce a follow-on
Atkinson, who is playing his first Test of the series following a hamstring strain, said that he is "ready to push the limits" in case Woakes does not take any further part.
Aiden Markram scored an unbeaten century as South Africa edged tantalisingly close to an unlikely success in the World Test Championship final, needing 69 runs to dethrone Australia after reaching 213-2 at stumps on the third day at Lord's on Friday.
South Africa completed an innings and 236-run victory over hosts Zimbabwe on the third day of the second Test on Tuesday to convincingly sweep the two-match series.
True to form, Pant brought up his seventh Test hundred in the most Pant-esque way possible, with a soaring one-handed six off Shoaib Bashir. A
South Africa beat Australia by five wickets to win World Test Championship
After hundreds upon hundreds of runs on flat tracks in the ongoing series so far, it took the green top at The Oval to finally produce the best day of the Indian summer, on the fifth and last Friday of the Test series.
Images from Day 3 of the fifth Test between Australia and India at the Sydney Cricket Ground on Sunday.
Australia's second-string pace attack produced a first-rate display to sink Pakistan with a comprehensive 29-run win in the weather-truncated first T20 International on Thursday.
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