The skirmish occurred in the fourth quarter at Milwaukee's Fiserv Forum after Antetokounmpo drove to the basket and was knocked down by Kanter, although no foul was called. Antetokounmpo ran back up the court and went face-to-face with Kanter before the two were quickly separated.
After a review, each player was called for a technical foul, then Kanter was called for a second technical, leading to an automatic ejection with 9 minutes, 56 seconds left.
Kanter, who was hit near his eye by a Thon Maker elbow on the previous play at the other end and eventually required three stitches, said he didn't know he was ejected until reporters told him after the game.
"I shot the ball and I was trying to go get the rebound, offensive rebound," Kanter said. "I think Thon Maker's elbow just glanced against my eye, and it started bleeding. And then on the other side, I think Giannis was driving the basket, and I stopped him. They didn't even call a foul. And then we just got into it a little bit.
"And then my eye was bleeding and they said, 'You need stitches.' So I went in the back, and the doctor just gave me three stitches. Now you guys are telling me I got ejected."
Referee Brian Forte said there were two situations that led to Kanter's ejection.
"During instant replay review for the altercation, we observed an unsportsmanlike act by Kanter, and that is what led to his first technical foul,'' Forte told a pool reporter. "After the out-of-bounds foul, Giannis and Kanter came face-to-face, and so they were both assessed dead-ball technical fouls."
With half a quarter to play and the Knicks within 91-82, Antetokounmpo said it was important he remained in the game.
"At the end of the day, I have to help my team and close out the game," said Antetokounmpo, who finished with 31 points and 14 rebounds. "We had like eight or nine minutes left, and I was just thinking about closing out the game. I just do not like when dirty plays happen that risk my health or my teammates' health. I don't like that."
During the altercation, Bucks assistant coach Darvin Ham came between Kanter and Antetokounmpo as the two players were being separated at midcourt.
After the game, Ham's involvement drew the ire of Knicks star Kristaps Porzingis, who said he didn't like seeing an opposing team's coach grab his teammate from behind.
"That was some bs tonight!!!" Porzingis, who is rehabbing a torn ACL, posted in an Instagram story. "And that bucks assistant coach needs to sit his ass down before grabbing Enes like that. Grab your own players not the opp. team."
Kanter also was critical of Ham, saying, "An assistant coach cannot football-tackle a player. The priority is to protect their players."
The Bucks, who got their sixth victory in seven games, swept the home-and-home series, having won at New York 109-95 on Christmas.
The Associated Press contributed to this report.