Clark, 28, was pulled over for a vehicle violation south of downtown Los Angeles at about 9:20 p.m. Sunday, LAPD public information officer Tony Im said.
Officers noticed a bag with an Uzi sticking out in plain sight in the car, Im said. Clark was then arrested on suspicion of having a concealed firearm in a vehicle.
He was booked into Los Angeles County jail and released Monday afternoon on $35,000 bond, according to the county sheriff's jail inmate website.
"We are aware of the matter, which will be reviewed under the NFL's personal conduct policy," NFL spokesman Brian McCarthy said.
Clark's attorney, Alex Spiro, said the gun belonged to Clark's bodyguard.
Clark was also arrested in March, along with another man, when officers said they found two loaded firearms in their vehicle after a traffic stop, The Kansas City Star reported, citing California Highway Patrol records.
A native of Los Angeles, Clark played his first four NFL seasons with the Seattle Seahawks before being traded to Kansas City in 2019. He was part of the Chiefs' Super Bowl-winning team in the 2019 season and has 49 sacks in 91 career games plus eight sacks in two postseasons with Kansas City. He has twice been named to the Pro Bowl since joining the Chiefs.
Clark was previously arrested in 2014 on suspicion of domestic violence over an incident at an Ohio hotel, leading to his removal from the University of Michigan team. He eventually pleaded guilty to a lesser charge of disorderly conduct.
The Associated Press contributed to this report.