According to the Warriors forward, the fan said "some threatening things to my life."
Green responded several times to the fan before running back to the other end of the court when play resumed. He said he almost got into it with the fan even more, but managed to keep his composure.
At the next stoppage -- a pair of Stephen Curry free throws at the 5:19 mark -- Green informed a referee what happened. The ref got security, and the fan was escorted out of the game.
In a statement afterward, the Bucks said the ejection was "under the referee's digression" and that they're "investigating the situation and we're conferring with the NBA."
Green, meanwhile, addressed what happened and how he handled it.
"Some people look at NBA players like they're superhuman," he said. "That they're this larger-than-life figure. So you come and you get someone to say something back and they get fined. They go home and laugh with their buddies.
"I think it's just one of those things when you can hold it in and get to the ref and get them out, it's great."
Tuesday wasn't the first time Green had an incident with a fan this season. Just over a week ago, he was fined $25,000 for a verbal altercation with a fan in Dallas.
After that Nov. 29 incident, Green told ESPN he wasn't sure what else the league could do that it hasn't already done to ensure good fan behavior and protect players.
On Tuesday, he reiterated that sentiment but made it clear he knows this isn't an issue the league ignores. Where he takes issue with the NBA is when "they jump and fine guys for saying something back ... I think when you see guys get fined, it's more often a license for more people to do it."
Green said he feels it would take something, or someone, outside of the NBA to make real change regarding fan decorum.
"There are no real consequences," Green said. "Yeah, you can't come back to the game, or even if you get arrested, nothing really happens ... you just hope it gets to a point where these leagues can work with legislators to implement laws, because that's the only thing that's really going to correct the issue."
ESPN's Jamal Collier contributed to this report.