The Belgium international has been suffering with a virus during the close season which has resulted in significant weight loss.
Fellaini has made fleeting appearances in Everton's pre-season games, although he did manage 90 minutes in yesterday's 2-2 draw at Coventry.
Moyes is unsure as to whether the 21-year-old will be fully recovered before the Premier League opener at home to Arsenal on August 15.
"Fellaini has had an illness for most of the summer which has affected him,'' said Moyes. "He picked up a viral infection in the summer. It got into his blood, he lost a lot of weight and he wasn't a boy that could afford to lose any weight.
"It's noticeable looking at him how thin he has become. It has definitely had an effect on his overall performance. It is going to take a little while I feel for him to get his full strength back. I don't think he is there yet.
"He has not been right all through pre-season and he is still not right. When you are the shape and build he is, when you lose weight it's not all that easy to put it back on.
"Since he has come back we've been trying to get him built up, but the weight is not going back on at the moment.''
In-demand defender Joleon Lescott will miss tomorrow's friendly at Blackpool because of a hip injury.
The England international, who also sat out yesterday's friendly, is wanted by big-spending Manchester City and the Toffees have already turned down two bids from the Eastlands club.
However, Moyes said Lescott's absence had nothing to do with the on-going speculation about the player's future.
"Joleon picked up a hip injury while we were in America,'' Moyes told the club's website. "We don't expect him to be fit for Tuesday but hopefully he can make it on Friday against Malaga.''