Coetzee has chicken pox, while Nxumalo has a hamstring injury.
The Bafana technical team is searching for their replacements.
Bafana Bafana will face Mauritania in their final 2017 Gabon Africa Cup of Nations qualifier on Friday, and they will be in action four days later against Egypt in the Nelson Mandela Challenge.
“Prince Nxumalo (hamstring) & Rivaldo Coetzee (chicken pox) have withdrawn from Bafana Bafana squad. Still working on replacements,” read a tweet from the national team’s official account.