Washington's WUSA-TV reports police in Fairfax, Va., said Babbitt, 65, was arrested about 10:30 p.m. Saturday after an officer observed a vehicle driving on the wrong side of the road. Babbitt was reportedly alone in the car.
Police said Babbitt cooperated with the arresting officer and was taken to the Adult Detention Center.
The U.S. Transportation Department said it didn't learn of Babbitt's arrest until Monday, CBS reported.
"Administrator Babbitt has requested, effective immediately, to take a leave of absence from the FAA," the department said in a statement. "That request has been granted, and Deputy Administrator Michael Huerta will serve as acting administrator.
"(Department of Transportation) officials are in discussions with legal counsel about Administrator Babbitt's employment status."
Babbitt has been head of FAA since 2009. He previous was chairman of the agency's Management Advisory Council, was an Eastern Airlines pilot for 25 years and was president of the Air Line Pilots Association. He also was a partner at the management consulting firm Oliver Wyman.
The Washington Post reported Babbitt was released on his own recognizance and will have a Feb. 2 court hearing.
The newspaper said a Fairfax police spokesman said the department doesn't release blood-alcohol levels of those charged or the results of roadside sobriety tests.
In an interview with The Hill reported last week, Babbitt called his job "fascinating," but that he didn't plan to seek another five-year term to the post.
"It's my first time serving in the public sector and I've worked with wonderful people," he said. "I'm serving a five-year term. When it ends, it ends."
In the article, Transportation Secretary Ray LaHood called Babbitt a "champion for safety."