The Colony police Sgt. Aaron Woodard said Kazee was booked on a Class B misdemeanor. Kazee was released around midday after posting $2,500 bond, Woodard said.
Kazee was pulled over in the suburb next to Frisco, the location of team headquarters about 30 miles north of Dallas. Kazee is in his first season with the Cowboys after signing as a free agent.
The 28-year-old has started all six games for the Cowboys (5-1), who have won five consecutive games. Dallas is off this week. Its next game is Oct. 31 at Minnesota.
On Monday, coach Mike McCarthy said he talked with players last week about being smart during the bye when he informed them they would not have any practices this week.
"Talked about the distractions and what we don't want," McCarthy said. "We have an outstanding season -- 5-1, where we are -- make sure that everybody is taking care of themselves and spend as much time as they can with family and friends. They deserve it. They deserve this break, the length of it. I have a lot of confidence and a lot of trust in those guys."
Kazee spent his first four seasons with Atlanta, and the fifth-round pick started 34 of 52 games with the Falcons. His arrival in Dallas coincided with that of defensive coordinator Dan Quinn, who was Atlanta's coach for five-plus seasons before getting fired last year.
The Cowboys had no comment on Kazee's arrest. His agent didn't immediately return a message seeking comment.
ESPN's Todd Archer and The Associated Press contributed to this report.