Neville's absence is a major blow to England's preparations for the World Cup finals in Korea and Japan which start on 31 May.
England coach Sven-Goran Eriksson, who will name his 23-man squad next Thursday, will now have to re-think his plans.
"It has happened too late, I guess. All we can do is wish Gary all the best for a full and speedy recovery," said Eriksson.
The England boss, in a statement released by the FA, added: "This is a cruel blow not only for Gary Neville but also for England.
"Gary is not just a very good football player but he has also been a loyal member of the team. I feel very sorry for him.
"Competing at a World Cup is the pinnacle of any player's career and there are not that many opportunities to take part in the finals.
"For Gary to lose out at this time is obviously a huge disappointment to us all."
Danny Mills, Owen Hargreaves, Jamie Carragher and Phil Neville are now competing for the right-back position in England's World Cup squad.
Manchester United defender Wes Brown could also come into the reckoning.