It was decided the versatile back should undergo surgery instead of playing in a dead-rubber match against the Springboks.
Rogers hopes to be able to recover from the surgery and get back on the training paddock, before the Wallabies' end-of-season tour begins in November, the Australian spring.
"Mat will have an arthroscopy on his knee this Thursday and will be required to rest for up to two weeks following surgery," said Wallabies team doctor Martin Raftery.
"He should be able to resume full training sometime between four and five weeks after the arthroscopy, which will give him the chance to prepare for the spring tour."
Western Force utility back Scott Staniforth will be Rogers' replacement in the 25-man Wallabies squad, which departs for Johannesburg on Friday following a three-day training camp in Sydney.
Rogers said that he was disappointed to miss out on the trip to South Africa, especially as he was being touted to get a run in the Number 10 jersey ahead of incumbent flyhalf Stephen Larkham.
"I've had (the injury) for a couple of weeks now and I was hoping it would have pulled up a bit better than it has (after the New Zealand Test)," said Rogers.
"I'm disappointed to miss out on the Springboks match because I feel that we've got a great chance of winning a Test on their soil, which hasn't been done for a long time," he said.
"Although by having the surgery now I'll have time to get a good preparation for the spring tour."