Tottenham have enjoyed an impressive start to the season, picking up 10 points from a possible 12 so far.
In August, Maddison scored one goal and provided two assists for his new club.
The £40m signing from Leicester City saw off competition from Brentford's Bryan Mbuemo, Jarrod Bowen of West Ham United, Brighton's Kauro Mitoma, Manchester City midfielder Rodri and Nottingham Forest's Taiwo Awoniyi to claim the honour.
Postecoglou was in contention with Mikel Arteta, Pep Guardiola, Jurgen Klopp and David Moyes for the managers' prize but the Australian emerged victor in his first month in English football.
"I've been nominated for the award a few times, so it's a nice feeling to actually win it!" Maddison said.
"It's never easy as a new player at a new club in the Premier League, so if you'd have offered me this at the start of the season, I'd have bitten your hand off!
"So many big names, elite players in the past and currently have won this award so it's nice to be in that category. This award will sit nicely on the mantelpiece!"
The England international added on his boss: "It’s a brilliant achievement for him in his first month as a Premier League manager."
"I’m sure he’ll say it’s all about the team but he's been brilliant with all the lads."
