Authorities say 21-year-old John Ellis Bush was arrested by the Texas Alcoholic Beverage Commission early Friday morning.
Bush was released on $2,500 bond for resisting arrest and on a personal recognizance bond for the public intoxication charge.
Gov. Jeb Bush says, "My son's doing fine. It's a private matter. We will support him.
We feel sad for him, but I'm not going to discuss it on the public square with 30 cameras."
John Ellis Bush is the nephew of President Bush.
A spokesman for Jeb Bush says the governor and his wife Columba are concerned about the incident.