Fellaini has not featured since the Red Devils' home defeat by Everton on December 4, since when he has been troubled by a back problem.
Moyes had thought the £27.5million Belgian would have recovered by now.
However, that has proved not to be the case and Fellaini will be missing again tomorrow when United entertain West Ham.
Moyes is going to send the former Everton man for another scan. And, if the results are not positive, it is likely Fellaini will have the wrist operation he has been putting off for a while but is likely to keep him out for a number of weeks.
"Fellaini has an injury to his back, which we hoped might have healed up but it hasn't," Moyes told reporters.
"I am going to get another scan and if it hasn't healed up then I might need to take the decision to get his wrist done as well.
"We hoped his back would be better in 10 days but he is still feeling it."
There is better news about Michael Carrick, who has not featured since the victory over Arsenal at the beginning of last month but should be available to face former club Spurs on New Year's Day after recovering from his Achilles injury.
"Michael has just started some work outside on the grass," said Moyes.
"He is getting a little bit closer.
"He is roughly due to be back at New Year's Day time. We might be able to squeeze a few more days out of it but I couldn't be sure yet."