The younger Paul, who also is the grandson of 2012 Republican presidential candidate Ron Paul, who left Congress this month, was arrested Saturday morning at Charlotte Douglas International Airport in North Carolina following a flight from Lexington, Ky., The Charlotte Observer reported.
Paul was charged with underage consumption of beer or wine, disorderly conduct, and being intoxicated and disruptive, the newspaper said.
"He was possibly served alcohol on the flight," Charlotte-Mecklenburg Police Lt. Blake Hollar said.
The elder Paul's office issued a statement in which the Republican senator from Kentucky sought privacy for a family matter.
"Sen. Paul is a national public figure and subject to scrutiny in the public arena," the statement said. "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."