Pukki, who has scored 30 goals for the Canaries so far this season, received the accolade ahead of Blues forward Che Adams and Sheffield United's Billy Sharp, who were also on the three-man shortlist.
Pukki said: "It's an honour to win this award, I'm really happy for the recognition.
"I have really enjoyed this season so far in what is a fantastic league, but we know there are still many big games to come.
"There are many great players here tonight, so it's special to win this award."
Luton Town’s James Collins won the League One Player of the Season award, with Tranmere Rovers’ James Norwood netting the top prize for League Two.
Meanwhile, Norwich City defender Max Aarons was named the EA Sports Young Player of the Season.