The incident occurred at 5:30 a.m. Thursday at the Birmingham-Shuttlesworth International Airport, AL.com reported.
According to authorities, the man, who was not identified, told police he was robbed in the area and wandered onto airport property, Birmingham police Sgt. Johnny Williams told the website.
The man was taken into custody, and police learned he had an outstanding felony probation violation warrant with Shelby County, located south of Birmingham, WTVM reported.
Passenger Stephen Reeves said he was on a Delta flight bound for Atlanta, and said the plane's captain made an announcement.
"The captain made an announcement that we were standing by because of an unauthorized person on the ramp," Reeves told AL.com. "I went back to reading and then the man in 1B pointed out the window and I saw what -- the man laying on the tarmac."
Reeves was one of several passengers who snapped photos of the incident and posted them to social media, the website reported.