Experiencing discomfort in his pelvis, the 23-year-old’s condition worsened during bowling on the third day of the match on Thursday, which South Africa won by an innings and 32 runs.
Scans conducted on Friday unveiled the severity of the injury, as confirmed by a statement from Cricket South Africa.
As of now, no replacement has been introduced to the squad.
Coetzee was part of a four-man seam attack for South Africa at Centurion where they bowled India out twice. But the second, and final, Test at Newlands in Cape Town will likely see the return of spinner Keshav Maharaj to the home line-up.