He dislocated his knee during Falcons' Guinness Premiership defeat against Gloucester at Kingsholm on Tuesday night.
Estimates about his recovery are that he is unlikely to play again before Christmas, ruling him out of England's autumn Test matches with the Pacific Islanders, Australia, South Africa and New Zealand.
Newcastle rugby director Steve Bates said: "Jonny has had his operation, and the reports are that it went well.
"They are optimistic about it, and we will have to see how it progresses.
"It is a reasonably difficult injury, and it will take a bit of time to come back.
"Jonny plays with 100 per cent effort, and in that respect he is very vulnerable, but he is just the same as everyone else."