The Belgian has been absent since the 1-0 home loss to his former club Everton at the beginning of December and Moyes admitted his recovery was taking longer than planned.
Fellaini will now be sent for a second scan to assess the extent of the injury and, if it is likely to keep him sidelined for an extended period, United will also take the opportunity to schedule an overdue wrist operation.
"Fellaini has an injury to his back, which we hoped might have healed up but it hasn't," Moyes said.
"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."
Fellaini moved to Old Trafford following a protracted transfer saga, initially involving a joint bid that included Leighton Baines.
He has struggled to make an impact since completing the transfer, however, and United are languishing in mid-table ahead of Saturday's visit of West Ham.
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