Los Angeles County sheriff's deputies say the incident began when a man backed his car into Brady's vehicle Sunday night in the 21200 block of Pacific Coast Highway.
The two drivers began exchanging information but when the other driver heard sirens approaching he reportedly tried to run away on foot, according to a sheriff's statement. Brady tried to stop him from fleeing and a scuffle broke out, deputies say.
The other driver was able to run away but deputies found him a short time later in a nearby neighborhood. They arrested the driver, whose name was not released, for suspicion of driving under the influence of alcohol, hit and run (property damage only), and battery.
Anyone who witnessed the confrontation or who has more information is asked to call the Malibu/Lost Hills Sheriff's Station at (818)878-1808.
Brady, 51, is an actor, singer, comedian and host of the game show "Let's Make A Deal."