Neville was stretchered from the field and club physiotherapist Mick Rathbone confirmed that the player could now be out for some time.
"An MRI scan on Monday morning has confirmed our fears and it has revealed that Phil has damaged ligaments at the back of his knee," Rathbone said.
"He will now rest it for 48 hours to allow the swelling to go down and he will then see a specialist in London before a decision is made on how best to manage the injury."
Neville sustained the injury following a second-half challenge with Fulham's Dickson Etuhu, which Everton manager David Moyes was unhappy with.
Neville's absence means the Toffees have problems at right-back for the visit of AEK Athens on Thursday, with new signing John Heitinga ineligible and Tony Hibbert suspended after being sent off in the second leg against Sigma Olomouc.
"It's too early to estimate length of absence but I fear he is certainly facing a lengthy lay-off," added Rathbone.