The batting all-rounder sustained a knee injury while playing for South Africa in the recent tri-series in Zimbabwe.
Duminy has, therefore, not even travelled to India with his team-mates.
His absence represents a major blow for the South African side given he is one of their leading stars.
The 30-year-old is the Cobras' second-most prolific batsman with 981 runs across 40 appearances.
Cobras begin their campaign against Northern Districts on Friday.
Duminy's injury is also a frustrating withdrawal for the event, with Dale Steyn and Mitchell Johnson having also pulled out.