CNN reported Monday that William Paul has been charged with underage drinking and disorderly conduct.
Rand Paul's communications director, Moira Bagley, released a statement Sunday requesting "privacy and respect" as the family deals with the matter.
"Sen. Paul is a national public figure and subject to scrutiny in the public arena; however, as many parents with teenagers would understand, his family should be afforded the privacy and respect they deserve in a situation such as this," the statement said.
Rand Paul, the son of recently retired Rep. Ron Paul (R-Texas), had his own legal showdown at an airport last January, when he was reportedly detained by Transportation Security Administration (TSA) officers for refusing to undergo a pat-down.
TSA said it followed its normal procedure with the Kentucky senator, who has often been sharply critical of the agency's policies.