Brown said Friday that a cousin he declined to identify posted the offending tweets after the game and said he has apologized to his teammates. The Twitter account has been deactivated.
Texas senior forward Gary Johnson said Brown's teammates have accepted his explanation and support him.
Coach Rick Barnes said he allows his players to have social media accounts, but warns them about being careful what they, or anyone else, posts.
Texas (21-3) plays Baylor (16-7) at home on Saturday.