A statement released by Scholes said: "It is with great regret that I have chose to leave the club with immediate effect".
The team have not won in six matches since beating Yeovil the night after the former Manchester United and England player took charge.
"It unfortunately became clear that I would not be able to operate as I intended and was led to believe prior to taking on the role".
"I hope to, at the very least, see out my initial term of 18-months as the manager".
Oldham are now 14th in League Two, having picked up just six points in seven games under Scholes, with his sole win coming against Yeovil Town in his first game as manager.
A number of members of the "golden generation" of English football have moved into management in recent times, with Frank Lampard and Steven Gerrard also taking their first jobs this season.
"The fans, players, my friends and family all knew how proud and excited I was to take this role".
The 44-year-old is a boyhood Latics fan, but has endured a poor start to his managerial career with the club, winning just one of the seven games for which he was in charge.
"We would like to place on record our thanks to Paul for his efforts during his spell in charge of the club and would like to wish him well for the future".