The 24-year-old suffered a knock in the first half of the Toffees' 2-2 draw with Oldham Athletic and had to be substituted at half time.
Anichebe has enjoyed a run in the team recently with Nikica Jelavic struggling in front of goal and repaid his manager's faith with three goals in four games.
Meanwhile, Seamus Coleman is back in contention following a thigh strain, but is unlikely to start at Carrow Road.
"We have only got a few [concerns]," Moyes told reporters. "Victor Anichebe, we have got a bit of doubt over him.
"Seamus Coleman is back in training, but apart from that most of them are okay."
The Blues are currently sixth in the Premier League.