Police were called to Nicholas Van Varenberg's apartment in Tempe, Arizona to investigate reports that he had punched an elevator.
But after 20 minutes after they left, his flatmate ran after the officers and told them the 21-year-old had held them at knifepoint, according to entertainment news website, TMZ.
The Hollywood star's son was said to have been angry his flatmate had let police into their apartment.
Officers searched the property and found marijuana and a knife.
Van Varenberg, who shares his father's real surname, was arrested on suspicion of aggravated assault with a deadly weapon, unlawful imprisonment, marijuana possession and possession of drug paraphernalia.
Born in Los Angeles, his mother is model and actress Darcy LaPier, Van Damme's third of four wives.
Van Varenberg appeared alongside his father in his first film, martial arts reboot Kickboxer: Vengeance, last year.
Van Damme, known for films including Double Impact and Bloodsport, has two older children.