Berry pleaded not guilty to murder and two counts of assault with a firearm.
Burton was in Los Angeles to complete his debut album, but never made it to the studio.
Police said Berry opened fire as the rapper waited for his car at the Beverly Center valet on Monday.
The gunman fled in a rented Mercedes, but witnesses were able to get a license plate number, and police quickly released an alert. Police found Berry at a ticketing line at LAX.
A lawyer for Berry said his client was acting in self defense and feared for his life after an altercation with Burton at an Atlanta nightclub earlier this month.
Berry remains in jail on $5 million bail.