Gibson missed three months at the start of the season before another setback around Christmas.
The former Manchester United midfielder has featured in the Toffees' last six games and Moyes hopes that he can continue as they push for a European place.
"I think we are in control of Gibson, but there is a danger," said Moyes.
"We thought he might need an operation earlier in the year but the medical staff have managed it well. We think we can get away with it just now, but he is going to need [an operation] sometime.
"I think he can offer more but maybe it is the injury holding him back a bit. He is going to have to get up and get on with it, and he has done that to be fair to him."
Everton's next match is against Reading this afternoon.