Postecoglou, whose side host Sheffield United on Saturday, guided new-look Spurs to wins over Bournemouth and Manchester United in August following the opening-day draw at Brentford, and beat competition from Arsenal's Mikel Arteta, West Ham boss David Moyes, Liverpool's Jurgen Klopp and Manchester City head coach Pep Guardiola to the award.
All five nominees were unbeaten but Guardiola was the only manager with a 100 per cent record from the month.
Maddison has been at the heart of Postecoglou's transformed, possession-based side and scored his first goal for Tottenham against Bournemouth, following it up with another in the 5-2 win over Burnley this month.
Spurs are aiming to maintain their unbeaten start against the Blades, with deadline-day signing Brennan Johnson in line for a debut.
Johnson only trained with Spurs for the first time on Wednesday after Wales duty so is more likely to be among Postecoglou's substitutes, depending on fitness checks for the club's other internationals.