The former Celtic flop scored five times in Norwich's first three games on returning to the top flight, including a hat-trick in the 3-1 win over Newcastle United.
His superb form continued over the international break with two more goals for Finland in the UEFA Euro 2020 qualifiers against Greece and Italy.
Pukki opened his Premier League account with a consolation strike in a 4-1 loss to Liverpool, which has compiled a perfect record after four games.
Reds boss Jurgen Klopp scooped the Manager of the Month award for leading the European champion to victory over the Canaries and defeats of Southampton, Arsenal and Burnley.
Liverpool faces Newcastle on Sunday (AEST) as Norwich entertains reigning champion Manchester City.