"It will be about two or three months, we're not putting any timescale on it," Fletcher said.
"He definitely needs to be inactive for four weeks and then he starts his rehab. He'll be back when he's ready - it will be around eight to 12 weeks."
England open their Six Nations campaign at home to Scotland on February 3 - in 13 weeks' time - and to be considered for selection Wilkinson will need to have had a run of games under his belt.
Wilkinson has not played for England since the 2003 World Cup and this freak injury - his 10th since landing that famous drop-goal in Sydney - is another bitter blow.
Wilkinson was named in Andy Robinson's elite England squad only to tear a medial knee ligament in his second competitive game of the season.
The Gloucester match was Wilkinson's comeback and he drew rave reviews for his performance. But he suffered the injury after 20 minutes and Wilkinson discovered that by playing on he may have made the injury worse.
"I don't think it really hindered the way I was playing. The annoying fact is that it seems that playing on may have made it a lot worse," he said.
Fletcher insisted Wilkinson does not have a chronic injury problem.
"This injury is very rare. It occasionally happens in boxing," said Fletcher.
"I think Jonny's injury record is bad luck. The two injuries he had this year - one was catching a high ball and someone hit him from the blindside. The other, one of our seconds rows fell on his leg."
If Wilkinson misses the Six Nations he will have just five England Tests - the summer tour of South Africa and the August warm-up internationals - before England's World Cup defence.