Drummond extended his arms as Antetokounmpo went up in the one-sided affair, leading to his ejection.
The Bucks were up 95-54 at the 4:07 mark in the third quarter when the foul occurred.
Drummond exited the contest with 12 points and 12 rebounds in 26 minutes.
Milwaukee went on to win 121-86 to take a 1-0 lead over Detroit.
Antetokounmpo was one of seven Bucks in double figures, finishing with 24 points and 17 rebounds in 23 minutes.
Game 2 will be played in Milwaukee on Wednesday.