Nche injured his pectoral muscle ahead of the thumping 43-12 Rugby Championship win over Australia in Pretoria two weeks ago, and Springbok coach Jacques Nienaber conceded on Thursday he faces another month "or so" on the sidelines.
Flyhalf Handre Pollard and captain Siya Kolisi are at this stage still on course to return from their injuries when South Africa play Argentina, Wales and New Zealand in World Cup warm-up games in August.
"Handre and Siya are on the road to recovery and if everything goes well, hopefully they can play in the Rugby World Cup warm-up matches. We can't predict for certain when they'll be back, but what I can say is that we won't push them," Nienaber told reporters.
"All three are players have done the job for us before and we know they'll be able to come back from injury and play."
Pollard and Kolisi were mainstays when the Boks lifted the World Cup trophy in Japan four years ago, but Nche missed out on selection for that tournament.
Victory in their final Rugby Championship fixture of the year at home to Argentina on July 29 will give South Africa a chance of winning the competition, but they will likely need Australia to beat New Zealand in Melbourne.
The Boks open their 2023 World Cup campaign against Scotland in Marseille on Sept. 10.
