Duminy suffered a hamstring strain in their game against Afghanistan.
The exact length for his recovery is unknown but South Africa are hopeful of having him ready for their final group game against Sri Lanka next Monday.
Scans confirmed the injury, team manager Mohammed Moosajee said.
Duminy has scored 83 runs in two matches without being dismissed, and also took 1-31 in the loss to England.
In Duminy's absence, South Africa will include Aaron Phangiso to complement the legspin of Imran Tahir with the wicket in Nagpur likely to suit spinners.
"Brandon Jackson, our physio, will have his work cut out for him. With these things you can't really put down a time frame. It could be anything from seven to 14 days," Moosajee said.
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