All-rounder James Faulkner will replace Cummins, who suffered lower back pain during the last one-day match against England earlier this month.
A scan on Wednesday showed up a new early stage lumbar bone stress fracture on the 22-year-old.
He has been plagued by injury, including a back stress fracture that ruled him out of the entire 2012-13 southern summer.
Cummins returned to first-class cricket with Australia A in July 2013, but suffered a recurrence of the injury and missed most of the 2013-14 domestic season.
Physiotherapist David Beakley said Cummins will go into a lengthy rehabilitation programme.
"This is really unfortunate for Pat... He is a young bowler with a bright future for Australia and we were really pleased with how he bowled in the UK," said chairman of the selectors Rod Marsh.
Faulkner, 25, who missed the ODI series in England after he was banned for drink-driving in Manchester in July, is a regular in Australia's limited-overs side.
He has also played just one Test so far, during the 2013 Ashes series.
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