Greaves took the helm after the departure of Karl Marginson, who had been in charge since the club’s inception in 2005.
A statement on the club’s website read, “Tom Greaves has resigned as manager of FC United of Manchester following the club’s disappointing start to the season.
“Tom’s resignation was received ahead of the club’s board meeting on Tuesday 28th August.”
Greaves added, “It has been an absolute honour, not only to play for the club but to captain and then manage it
“It is something that I will never forget and an experience that I’ve learnt a lot from both on and off the pitch.
“The opportunity to play football all over the world has been incredible and I will walk away with literally hundreds of special memories and that is largely down to the amazing fans of this club”.
Dave Chadwick will take temporary charge of the Red Rebels.