"Why even comment before you know what you're talking about?" the billionaire investor said in an interview on "Squawk on the Street."
Cuban said the NFL has always been involved in politics at some level.
Trump's criticism on Twitter of players who kneel during the national anthem sparked angry protests around the NFL on Sunday.
The president on Sunday told reporters the protests were "very disrespectful to the flag," and that owners should do something about them. He also insisted his position was "not about race," even as much of the criticism directed at him carried racial overtones.
"Just because you have a Twitter account doesn't mean you have to use it," Cuban said. "Just because you can say something, doesn't mean you should."
When asked whether he thinks the president is going to apologize, Cuban said: "The president is not going to apologize. Are you kidding me? The president should read a book."
"If he dishes it out, he's got to be able to take it," Cuban added.
Cuban, who supported Democrat Hillary Clinton in the 2016 election, has criticized Trump over issues and Trump has blasted Cuban likewise.
Trump on Sunday called for fans to demonstrate their own form of protest — by boycotting NFL games unless the league fires players who kneel during the national anthem.
"This is nothing new. We want to listen to the players' feedback," Cuban said. "The only thing that's changed now is the president is getting involved."
Cuban said he has always tried to be open with players about what their feelings are and how they want to participate in the community.
The firestorm started when then-San Francisco 49ers quarterback Colin Kaepernick kneeled during the national anthem last season to protest the treatment of African-Americans in the United States. He is no longer in the NFL.