Manager David Moyes confirmed in a press conference after his team's Barclays Premier League defeat at Reading that former England international Neville had surgery on Friday.
The news is a blow to a team already without Neville's fellow midfielder Darron Gibson, who missed a 10th successive match with a thigh problem on Saturday as Everton lost 2-1 at previous winless Reading.
Moyes admitted that Neville's influence was missed as Reading fought back to win their first league game of the season.
"He (Neville) had an operation on his knee that could keep him out for six to eight weeks," he said.
"His leadership was missed but we were missing quite a lot of senior players and you could see that by our bench. Thomas Hitzlsperger did OK, not too bad."
Everton are likely to be without 35-year-old Neville for a number of key matches in the coming weeks as they prepare to face Arsenal, Manchester City and Tottenham before Christmas.