Manager David Moyes confirmed that his club skipper and former England utility player Neville had surgery the day before the Premier League fixture at Reading.
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 as the Toffees lost 2-1 at the previously winless Royals.
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 yesterday 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 today 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.