The incident happened midway through the fourth quarter of the Bulls' 100-97 win after a basket. The Bulls led 78-76 at the time.
The pair exchanged some heated words, going forehead to forehead with one another. Nene then grabbed the back of Butler's head, and a scuffle ensued.
It didn't appear that punches were thrown, but after the officials reviewed tape of the altercation, Nene was thrown out of the game and Butler was given a technical.
"It looked like an MMA move to me. It was one of those headlocks," said Mike Dunleavy, who led the Bulls with 35 points -- one short of his NBA best. "It was great that Jimmy kept his cool. I think a lot of people put in that situation would've started throwing blows."
Asked about the possibility of being suspended by the league for Sunday's Game 4 in Washington, Nene replied: "I don't know."
"I have nothing to regret," he said. "I'm a warrior right there. What I did, I'm supposed to do."
Game 3 was the most physical meeting of the series to date. Both teams had been exchanging words and hard fouls throughout the night.
The Wizards lead the series 2-1.
Butler said he and Nene were just "competing" before words were exchanged and things got heated.
"I guess he gave me one of those [shoves] and I didn't like it. It is what it is," Butler said.
The young swingman said it was difficult for him to keep his composure during the situation.
"It is," Butler said. "But I knew I had to. I didn't want to get ejected like he did, nothing like that, but I can't back down from anybody. It's just not in me."
Butler was surprised things escalated so quickly.
"I didn't think it was that serious," he said. "But obviously he thought it was. I was just saying, 'Watch all of that, it was uncalled for,' but I'm not mad at him for it. He's a competitor -- I respect the guy."
After Nene scored a basket to get Washington within 78-76, he turned to run down the court, and he and Butler made contact. Butler put a hand on Nene's side, and Nene swatted it away. They then stood right in front of each other, talking, until Nene reached out to grab Butler. That's when other players stepped in to separate the pair.
"It was a turning point," Chicago's Joakim Noah said. "Emotions were riding high, and just got to keep your composure. You know, I'm not the one to talk; I've been in those situations. But it definitely was a bonus for us to have him out of the game."
Nene wouldn't say what Butler might have said to generate that sort of reaction.
After the fracas, Butler made a 3 to bump Chicago's lead to five points. He hit an even more important 3-pointer with 24 seconds left to break a tie and make it 94-91. He finished with 15 points, after scoring a total of 21 in the first two games.
Nene, who left with 10 points and four rebounds, indicated he thought it wasn't fair that he was kicked out of the game and Butler wasn't.
"We can't really talk about 'what if.' He is a big part of what we do," Wizards forward Trevor Ariza said about Nene, "but if he's not on the court, we need to find ways to win."
Information from ESPNChicago.com's Nick Friedell and The Associated Press was used in this report.