The 26-year-old was hit in the head with a bottle during an altercation outside of a club in Miami, sources told The Athletic's Shams Charania.
"He had no prior knowledge of or interaction with the assailants. He suffered facial lacerations but will make a full recovery," the Rockets said in a statement.
The NBA is looking into the events that transpired Sunday.
"We are in the process of gathering information and hopeful that Sterling makes a full recovery," a league spokesperson told Charania in a statement.
Brown was already ruled out of Monday's matchup against the Miami Heat due to a sore left knee suffered prior to the incident. He's missed the Rockets' previous four contests but accompanied the team on their current two-game road trip.
"I have spoken to him, and he's doing better ... Thankfully, he's gonna be OK," Rockets head coach Stephen Silas told reporters prior to tipoff Monday, including Mark Berman of Fox 26 Houston.