Officials said Cummins had suffered a "slight side strain" and was now doubtful for Wednesday's match against tournament debutants Afghanistan in Perth.
Cummins scored seven not out and took two for 38 from 6.1 overs on his tournament debut during Australia's dramatic one-wicket Pool A loss to fellow co-hosts New Zealand at Auckland's Eden Park on Saturday.
The 21-year-old fast bowler gave an Australia squad already facing injury problems a fresh scare when he went over on his right ankle with just his fourth ball after slipping in his delivery stride.
On Saturday, he got up quickly and continued bowling before New Zealand's Kane Williamson drove him back over his head for the winning six.
A Cricket Australia spokesman said Cummins reported an issue after the New Zealand game on Saturday but scans showed "nothing serious".
Cummins's career has already been beset by injuries, while Australia's World Cup campaign has seen the likes of skipper Michael Clarke, who also made his 2015 tournament debut in Auckland, and all-rounder James Faulkner sidelined.
Should Cummins be ruled out of Wednesday's match it would open the door to fellow fast bowler Josh Hazlewood, while Australia could make another change to their side if big-hitting all-rounder Faulkner comes through Monday's net session unscathed.
Australia, one of the pre-tournament favourites, opened their World Cup campaign with a thumping 111-run win over arch-rivals England but their last two Pool matches have ended in a no-result wash-out with Bangladesh and last weekend's nailbiting loss to New Zealand.
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