Mikel Arteta joined Everton's casualty list following Wednesday night's 1-1 draw with Birmingham. The Spanish playmaker had to be substituted within the first 10 minutes of the Premier League match at Goodison Park having sustained an apparent hamstring problem.
The midfielder has been in impressive form of late and was named captain for the game.
"It's too early to say - I'm not sure but I'm guessing he will be out for a few weeks."
Moyes admitted the loss of Arteta so early in the match was a major setback.
"It was a big blow for us because we needed some creativity and I knew that if we didn't have him, we would be struggling to create too much," Moyes said.
"Leon Osman did, but we were struggling otherwise really to make anything happen."