Chelsea boss Antonio Conte had been the only previous coach to win the award three times in a row during Chelsea's title winning campaign last season.
To win the December prize, Guardiola topped a six-man shortlist that also included Conte, Everton's Sam Allardyce, Roy Hodgson of Crystal Palace, Liverpool's Juergen Klopp and Tottenham Hotspur manager Mauricio Pochettino.
Kane scored eight goals in six matches last month, including back-to-back hat-tricks against Burnley and Southampton, to finish 2017 with a record tally of 39 Premier League goals.
The 24-year-old is now level with former Liverpool and England midfielder Gerrard with six player of the month awards, the most for any player in the competition's history.
Kane claimed the prize ahead of seven other nominees - Chelsea's Marcos Alonso, West Ham United's Marko Arnautovic, Liverpool duo Roberto Firmino and Mohamed Salah, Jesse Lingard of Manchester United, Leicester City's Riyad Mahrez and Manchester City's Nicolas Otamendi.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)
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