Knight, the 49-year-old co-founder of Death Row Records, was booked early on Friday (local time) and was being held in lieu of a $2 million bail, the department said.
The incident on Thursday afternoon took place after a man fitting Knight's description drove up to a burger shop in Compton, south of downtown Los Angeles, and began arguing with two people outside, Los Angeles County Sheriff's Lieutenant John Corina said.
The driver then backed into one of the two, before running them both over in a red Ford F-150 Raptor pickup truck and fleeing, the department said in a statement.
Knight had been involved in an earlier altercation with the same two people, Corina said.
One of the two struck died in hospital, the Sheriff's Department said. The condition of the second person, who was hospitalized, was not made public.
Before his arrest, Knight arrived at the sheriff's department West Hollywood station accompanied by his attorney to take questions from detectives.
"Homicide Detective have arrested Marion 'Suge' Knight for Murder," the department later said in a statement.
Knight will not appear in court on Friday, and the earliest he could be brought before a judge would be on Monday, said Jane Robison, a spokeswoman for the Los Angeles District Attorney's Office.
"I feel strongly that Mr. Knight did not do anything wrong in this matter. He was attacked by a number of individuals, that's already been corroborated by certain witnesses," Knight's attorney, James Blatt, told television station KTLA.
In November, Knight pleaded not guilty to a criminal charge stemming from accusations he stole a camera from a celebrity photographer in Beverly Hills. He was later released on bail.
A few months earlier, Knight was shot and wounded inside a West Hollywood nightclub along with two others during a party ahead of the MTV Video Music Awards.
Death Row Records was a leading rap label in the 1990s, featuring artists such as Dr. Dre, Tupac Shakur and Snoop Dogg.
However, Knight's hip-hop empire declined after he went to prison for a parole violation, Shakur was shot to death and Dr. Dre left the label.
