The Liverpool boss guided his team to a perfect start in their opening four matches of 2019-20 with wins over Norwich City, Southampton, Arsenal and Burnley.
That run secured the monthly accolade for Klopp, who saw off competition from fellow nominees Pep Guardiola, Roy Hodgson and Brendan Rodgers.
It is the fourth time he has been named Premier League Manager of the Month, having also taken the award in September 2016, December 2018 and March 2019.