Athena Hernandez, another MWAA spokeswoman, said the officer realised it was Spacey after he asked for a driver's licence. The incident came to the attention of airport authorities when the officer reported it to his supervisors, officials said.
The officer also noticed that when he pulled Spacey over there were other vehicles behind him that appeared to be camera crews following and filming him, officials said.
"This incident was unique because he was being followed by people," Hernandez said.
She said that she didn't know whether Spacey regularly flies out of Reagan National and that he didn't receive an security escort from airport personnel.
Hernandez said it is "not uncommon for a driver to receive a verbal warning." She added that it "just depends on the degree of the infraction."
"The officer determined a verbal warning would suffice and Mr Spacey continued on his way without any further incident," she said.
Juliane Balliro, a lawyer for Spacey, did not immediately return a phone call and email for comment.
Spacey, a two-time Academy Award winner, was a star on the popular Netflix show House of Cards, which has been filmed in Baltimore.
He has faced a number of sexual misconduct allegations in the past year in London and Los Angeles, although no charges have been filed. Netflix removed him from the final season of House of Cards following the allegations.