The 32-year-old has not played since England's tour to New Zealand in June and initial hopes the problem would cure itself have not come to fruition.
A specialist has now confirmed Johnson will need to be operated on - sidelining him for a further 10-12 weeks and forcing him to miss his country's forthcoming fixtures against New Zealand, South Africa, Samoa and Australia.
The news comes as a further blow to England coach Stuart Lancaster - who signed a six-year contract extension on Wednesday - with Alex Corbisiero (shoulder) and Geoff Parling (concussion) also out of the November internationals.
Despite the lengthy lay-off, Exeter head coach Rob Baxter does not believe Johnson's chances of making the England squad for next year's Rugby World Cup on home soil will be affected.
"I don't see any reason why he can't play himself into contention for England," he said. "The important thing is to perform with quality and to do that you need to be fit, you need to be strong and you need to feel comfortable with your body.
"It all sounds a negative when you’re not playing, but this could work out to be a positive for Tom because he’ll be confident going into contact and feel fit, feel fresh and feel strong."
Johnson, who has eight international caps, will also miss the majority - if not all - of Exeter's pool matches in the European Rugby Challenge Cup.