The 25-year-old Honduras international can now feature for Alan Knill's men in the final four games of the campaign.
He has made four appearances since joining United and scored the winning goal in Saturday's vital 2-1 victory at Crystal Palace.
Nunez told the club's official website: "I'm delighted to stay here until the end of the season. I've said it during my time here that I'm having a great time.
"I'm playing as part of a team with everything to play for and they're doing a good job.
"Initially I would have like to have signed for the club until the end (of the season) back in March."
Source: PA