During Saturday's TNT halftime show, Barkley said NBA Commissioner Adam Silver has to suspend Sterling if the league proves it's him on the tape making the statements.
"This is the first test of Adam Silver. He's got to suspend him right now. First of all, they've got to prove that's his voice on that tape. But this is the first big test for Adam Silver.
"You can't have this guy making statements like that. You have to suspend him and fine him immediately."
Barkley went on to say that someone in a position of authority in the NBA, such as a team owner, cannot be allowed to make racist statements.
"If someone wants to be racist, fine," Barkley said. "That's their thing. When you're in a position of power and you can take jobs and economic opportunities from people, that's what crosses the line. We can't have an NBA owner discriminating against a league — we're a black league. We are a black league."