The Liverpool boss ensured his side maintained their flawless start to the top-flight campaign by presiding over victories against Newcastle United, Chelsea and Sheffield United.
It's the second month running Klopp has been awarded the prize after also claiming it for August.
In clinching September's edition, the German saw off competition from Eddie Howe (Bournemouth), Frank Lampard (Chelsea) and Brendan Rodgers (Leicester City).
Klopp has now won the Premier League Manager of the Month award on five occasions, having also taken it in September 2016, December 2018 and March 2019, in addition to this season's two accolades.