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Police said 23-year-old Aubrey Louis Berry of Georgia was arrested at Los Angeles International Airport with a gun Monday night. His bail is set at $1 million.
Berry allegedly pulled a gun out during the argument and shot Burton in the head, then fled the scene.
"After finally the third gunshot, was when everybody was running, so everybody just kind of ducked down and ran inside P.F. Chang's," said witness Del Vaughn Walker.
It's unclear what the two men were arguing about.
A search followed involving LAPD and the Beverly Hills Police Department because police thought the suspect might be headed into Beverly Hills.
Instead, the suspect fled straight to LAX, where airport police found him in a ticket line. The suspect put his hands in the air and said, "I have a gun in my waistband. Please don't shoot me." He was taken into custody without any problems.
Burton was a 21-year-old Atlanta-based rapper who had worked with Akon on two rap singles, and was working to release his second album. He had also worked on the 2006 soundtrack for the movie "Step Up," had reportedly modeled for Diddy's Sean John clothing line, and was signed to Jive and Electra recording labels.
Burton was transported to Cedar-Sinai Medical Center, but later died.
"Too many mothers, too many brothers, too many fathers, too many uncles, too many sisters are losing their children," said the victim's uncle Eddie Pryor.
"This has got to stop."
The Associated Press contributed to this story.