The Dundalk striker, who returned from Scotland for a second spell at the club earlier this year, proved the match-winner in the FAI Cup final – scoring a superb hat-trick to see off Shamrock Rovers after extra-time.
A brace against Rapid Vienna in the Europa League also saw the 32-year-old, who celebrated his birthday this week, equal the record for most goals scored by a League of Ireland player in European competition.
Dubliner McMillan is currently level with Bohemians legend Glen Crowe on 11.
Dundalk team-mate Chris Shields finished second in the voting for the final Player of the Month prize of 2020, while Shamrock Rovers midfielder Aaron McEneff was third.
The Personality of the Year and Goalkeeper of the Year awards will be announced later this week.