The incident was reported just before 1 p.m. near Wilshire and San Vicente boulevards.
According to the Beverly Hills Police Department, the victim and the suspect, identified as 54-year-old Christopher Cornelius of San Bernadino, got into some sort of verbal altercation.
"During the altercation, [Cornelius] struck the victim multiple times with a metal object, then got into his vehicle and drove into the victim, running him over," police said in a statement.
The victim, who was not identified, was sent to Cedars-Sinai Medical Center where he later died.
Meantime, police said Cornelius ran to a nearby building after the incident but was quickly detained by officers.
Video posted to social media shows a white car driving the wrong way on Wilshire Boulevard before running over a man on the ground and taking off.
An anonymous witness said he heard a "loud argument" and looked out from his office window to see two men fighting in the street. He said the attacker was hitting the victim with what looked like a stick or pipe.
"It looked like he was maybe even trying to kill him," the witness said.
Another witness told Eyewitness News she was sitting in her parked car when the vehicle ran over the victim.
"I personally did not want to witness this person being dragged under the car, so I put my head down, but I was in the car and had felt this person's head likely hit the back of my tire and then the car sped off," she said.
Video from the scene shows officers taking a man into custody near the crime scene.
Witness Isaac Contreras said police "came out with shotguns."
"They flew a drone inside of the garage, and I think that's how they found where he was at," Contreras said.
It's unclear if Cornelius and the victim knew each other.
Cornelius was booked into the Beverly Hills jail on suspicion of murder. His bail is set at $2 million. Police said he has an "extensive criminal record," including violent crimes.
Anyone with information on the incident is asked to contact BHPD at 310-550-4951. If you'd like to remain anonymous, you can text "TIP BHPDALERT" followed by the information to 888777.