"At this stage, Pat is unavailable for selection for tomorrow's game," Clarke told reporters in Perth on Tuesday.
Selectors have yet to decide on the 11 to take on non-test playing nation Afghanistan, Clarke added, saying they needed to see how the team recovered from Tuesday's training.
Batsman Steven Smith was struck on the hand in the nets on Tuesday, but returned for another bat and was available for selection, Clarke added.
Cummins' injury opens the door for Josh Hazlewood to join left-armers Mitchell Starc and Mitchell Johnson on the WACA's fast and bouncy wicket.
The 24-year-old Hazlewood was replaced by Cummins after going wicketless in the big win over England in their World Cup opener in Melbourne.
Fast-bowling all-rounder James Faulkner has also declared himself fit for his first World Cup match after recovering from a side strain, placing further pressure on the misfiring Shane Watson.
If Watson was left out of the side it would likely mean a promotion for Smith to the all-rounder's number three position in the batting order, with Faulkner and fellow all-rounder Mitchell Marsh to bat lower down.
Australia are keen to hit back against minnows Afghanistan after the narrow defeat to New Zealand, which came after their second match against Bangladesh was washed out.
(Reporting by Ian Ransom in Melbourne; Editing by Peter Rutherford)
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