Injury-prone Cummins reported a "slight side strain" after making his World Cup debut in the one-wicket loss to the Black Caps on Saturday but scans revealed "nothing serious", a team spokeswoman told reporters in Perth on Monday.
The 21-year-old, who took 2-38 against New Zealand, will be monitored by team medical staff ahead of Wednesday's match against Afghanistan with Josh Hazlewood likely to replace him if he is not passed fit to play at the WACA.
Faulkner, meanwhile, told a news conference that he would be fit to face the Afghans if he got through Monday's training session without further mishap.
The 24-year-old suffered a side strain in the one-day tri-series final against England in Perth in early February and has missed both of Australia's matches so far.
"I'm going to bowl half a dozen overs today and if I get through that, I'll be available for selection and hopefully I'll get picked," he told a news conference at the WACA.
"I've been batting since two or three days after the injury to be brutally honest. Being a right-handed batter and left-handed bowler, it's not the same side."
But for his injury the left-arm seamer would have been one of the first names on the team list after his form this season, not least the unbeaten 24-ball 50 he scored in his last outing to drive Australia to victory over England.
Australia need a victory over the Afghans to kickstart their campaign after their second match against Bangladesh was washed out and their batting line-up was skittled for 151 runs in 32.2 overs by New Zealand at Eden Park.
"We all know we didn't perform as well as we could over in New Zealand and that's probably just going to make the team hungrier," Faulkner said.
"So far we've been very successful as a team and you're going to come across these little setbacks from time-to-time. Hopefully we can get back on the winning path on Wednesday."
(Reporting by Nick Mulvenney; Editing by John O'Brien)
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