Mbonambi, who limped off early in the World Cup win over New Zealand in France last month, has a knee injury that could keep him out until May. Koch, who was left out of the final because of a knee injury, faces a three-month lay off.
Both front rowers play for the Sharks in the United Rugby Championship, and their absence was confirmed by coach John Plumtree ahead of Saturday’s home match in Durban against Irish side Connacht.
The Sharks are looking to record their first win of the season, having lost their opening four matches in the competition, but their hopes are tempered by the fact they cannot use any of their sizeable Springbok contingent.
The South African Rugby Union has stipulated a mandatory three-week rest period for the players after their return from France.
"With someone like Eben Etzebeth, I can understand, and obviously Ox Nche and others who played a big part in the key games at the World Cup. Those guys do need a rest because of their heavy work load recently," Plumtree told reporters.
"However, I think it should have been done on an individual rather than on a blanket basis as there are some players who really need to be playing after not being utilised much."
He singled out the case of scrumhalf Jaden Hendrikse.
"An example is Jaden Hendrikse, who hardly played at the World Cup and in the warmup games, and was out of rugby before that after being injured in March," he said. "How is it helping Jaden’s rugby for him to be off the field when he has already been out for a long time?”