The pair, who played together at the Los Angeles Lakers between 2010 and 2012, were involved in an altercation last October over Fisher's friendship with Barnes's estranged wife Gloria Govan.
Barnes and Fisher came face to face on the court for the first time since the incident on Saturday night, a clash the Grizzlies won 103-95, and although the two appeared not to interact, Barnes's remarks in the media in the run-up to the game provoked the NBA to intervene.
"Every man who looks at the situation knows what's right and wrong," Barnes had told reporters. "Violence is never the answer, but sometimes it is. And unfortunately, it happened.
"I don't regret it. Like, man to man knows who's wrong and who's right. The NBA decided to step in and did what they did. But it is what it is."
In an interview with the New York Daily News, he added of Fisher: "I just don't like him, plain and simple. He knows I don't like him. Don't say nothing to me, I don't plan on saying nothing to him. Don't try to shake my hand. There's none of that. There's nothing there. There never will be. Just stay away from me basically."
The NBA has fined Barnes $35,000 (£24,500) for his comments.