Police ticketed Robert Crockett for hitting Quivers's car while driving in New Jersey on Sunday and then fleeing the scene.
Authorities were later able to track down Crockett after receiving information from several people who witnessed the crash, The Press of Atlantic City reports.
Crockett has been cited for leaving the scene of an accident, failure to report an accident, reckless driving and operating an unregistered vehicle.
Quivers later told Stern's radio audience that she's lucky to have escaped the accident uninjured, but insisted that Crockett "almost killed" her.
She joked: "Thank God I was in my SUV!"
Quivers first joined The Howard Stern Show in 1981 as a news anchor, eventually becoming one of the radio programme's longest-running contributors.
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Watch Robin Quivers's recent interview on Jimmy Kimmel Live below: