The Wimbledon Independent Supporters Association (WISA) claim MK Dons "stole" their club's place in the Football League but have decided against boycotting the fixture.
AFC Wimbledon have already stated they will not accept any boardroom hospitality from the League One club for the match in Milton Keynes - feelings are still raw after the original Wimbledon club relocated to the Buckinghamshire town and changed its name but maintained the 'Dons' from the old nickname.
A statement from WISA said: "We are naturally disappointed that AFC Wimbledon will have to play Milton Keynes, a football franchise, that stole Wimbledon's original league place, in the second round of the FA Cup.
"After careful consideration, WISA has decided not to formally request a boycott of the fixture by Wimbledon supporters."
The fans' group welcomed the decision by the League Two club to not accept boardroom hospitality at the fixture. WISA chairman Simon Wheeler added: "This is a fixture that very few Wimbledon supporters want.
"This fixture is a result of AFC Wimbledon's phenomenal successes over the last 10 years and must be incredibly embarrassing for those in Milton Keynes to be involved in. We don't see this fixture as a big grudge or rivalry match, but as one that should never have been allowed to happen."