Fellaini was caught by a two-footed tackle from Sotirios Kyrgiakos during the 1-0 loss but the full extent of the injury has only just been discovered after the Belgium midfielder visited a specialist.
"He has a very serious injury and needs an operation... so he will be out for six months," Moyes said ahead of Everton's Europa League clash with Sporting Lisbon. "It looks like it is the same as Robin van Persie's [injury]."
Fellaini had been criticised in some quarters for failing to recreate the form that saw him named Everton's 2008-09 Young Player of the Season after an impressive debut campaign.
But the 22-year-old had started to show an improvement in his form before the tackle from Kyrgiakos - for which the defender was sent off - ended his season prematurely.
Speaking last week, Moyes admitted having Fellaini out for any length of time would be frustrating.
"He's got a really bad ankle," Moyes said. "I was really surprised - it was like an elephant's ankle, it was that bad. He has been integral part of how we have played in recent weeks and he will be a miss."
Everton have been plagued by injuries over the past couple of seasons but with Mikel Arteta and Phil Neville returning recently, and Phil Jagielka closing in on a comeback, the blow has been eased somewhat.