In Monday's game between the two teams, Pachulia tangled with Babbitt after a missed free throw in the fourth quarter. He responded by striking his opponent in the face, resulting in a flagrant-1 foul.
The Heat went on to win 105-102, snapping the Warriors' seven-game winning streak in the process.
Pachulia is in his first season with the Warriors and enters Wednesday averaging 5.9 points and 6.1 rebounds per game despite averaging just 18.9 minutes.
While his presence has helped provide some balance to the Warriors in the low post, questions remain about his physicality. The 32-year-old has earned two technical fouls and three flagrant foul calls already this season.
Less than a week before the Babbitt incident, Pachulia made headlines due to a flagrant foul on Oklahoma City Thunder star Russell Westbrook. The MVP candidate didn't take it lightly, via SportsCenter:
With Draymond Green already having a propensity for picking up technical and flagrant fouls, the Warriors don't need another frontcourt player behaving in this way going forward.