The ex-Latics striker, 56, substituted Richie Wellens to some yearlong bargain in June after relegation to League Two.
Oldham, who have been unbeaten in six league matches before successive beats Exeter and Carlisle, are 12th in League Two and seven points away from the playoffs.
As they start looking for a replacement, pete Wild will simply take over as caretaker boss.
“We’d want to put on record our thanks to Frankie for his or her efforts during his time at Boundary Park,” a club statement said.
Before his appointment, Bunn had coached at a few clubs but had never obtained charge of a team at the English Football League.
Wednesday’s defeat away at Carlisle was the loss Bunn scrutinized in his 31 matches.
Oldham following face Port Vale in League Two on Saturday, before shooting on bottom club Notts County on New Year’s Day.