Kansas Turnpike spokeswoman Lisa Callahan said Morningstar was stopped early Saturday on the Kansas Turnpike near the East Lawrence interchange.
He was arrested and booked into the Douglas County Jail. Online jail records show he was released on $250 bond later Saturday morning.
The arrest is the latest embarrassment for the Jayhawks, who are expected to be ranked as high as No. 1 in the preseason poll. It comes as university police open an investigation into last month's brawl involving members of the school's football and men's basketball teams.
Kansas coach Bill Self said the team is still assessing the incident, but Morningstar, a returning starter, used "extremely poor judgment" in breaking team rules that had gotten tougher since the fight. He said Morningstar would remain part of the team, but would not be allowed to play in games or travel.
"Regardless of the details that concern the reason for him being stopped, he broke team rules that have been much more stringent since last week. Brady was in serious violation of curfew," Self said. "We will support him through this, but needless to say I am very disappointed in the sequence of events that took place last night."
Information from The Associated Press was used in this report.