The centre-back, who has captained England up to Under-19 level, will now return to Carrington following his stint with the National League side.
Fish made his United first-team debut in the 2-1 Premier League win at Wolverhampton Wanderers last May, in the final game of the Premier League season, and will now spend time with the Academy before determining the next step in his development at the club.
The Under-23s' next Premier League 2 fixture is at Leigh Sports Village, against Tottenham on Monday night, kicking off at 19:00 GMT.
United have been busy this week in the loan market, with central defender Teden Mengi joining Birmingham City until the end of the season and right-back Ethan Laird agreeing to switch from Swansea City to Bournemouth in the Championship.