Soppitt took charge of Esh in the summer of 2011 and guided them to a mid-table finish, but this season have failed to rediscover the same form, and lost 5-0 at home to Thornaby last Saturday.
Club secretary Dave Thompson said: "Matters have not worked out this season as well as Andrew would have liked, result of late have been disappointing."
Esh did have a good run to the Second Round of the FA Carlsberg Vase, where they lost 4-2 at Baris Northern Counties East Leaguers Parkgate.
Brian Maitland, who has managed several Northern League clubs in the past, is taking over until the end of the season.
Meanwhile, striker Ian Ward has left Esh for Durham City.
Credit: Ray Simpson