The Everton boss has admitted that the 25-year-old midfielder will "probably require an operation at the end of the season" to fix a persistent thigh problem
The problem forced the Republic of Ireland international to miss nearly three months from September 2012 onwards, and despite returning as a regular name in the side's starting 11 once he returned from injury earlier this year, he is seemingly still suffering.
Gibson scored only his second goal for the club since moving from Manchester United in January 2012 in Everton's 2-0 victory over QPR on Saturday, and Moyes believes that the 25-year-old has the ability to score more often but his thigh problem means that he is not currently able to do so.
"After the game on Saturday, I was asked about Darron Gibson's goal and his shot - I think he could do it more and with more ferocity as well because he's got a great shot on him," Moyes told reporters.
"He has got a bit of a problem at the top of his thigh which will probably require an operation at the end of the season."
Despite his injury, Moyes hailed the difference Gibson has made to his side, and insists he is currently in good form as Everton embark on an important final six games of the Premier League season.
"What he has given us is that he is good on the ball and he has a better range of passing than maybe some of the other midfielders we have," Moyes continued.
"I think overall he has had an impact. He had a bit of a dip midway through after he came back from injury but his form is good right now."