Christopher Mackrodt, 31, is accused of holding the woman for about three hours starting late Monday before letting her go, Nassau police said.
The suspect - a car mechanic - was not accused of physically attacking the woman, police said.
"I don't know what his motive was," said Insp. Jay Caputo, of the Nassau police detective division.
The two had apparently been together earlier inside a Levittown bar, said Det. Lt. Louis Monteleone of Nassau's 8th squad.
"They were engaged in conversation inside the establishment," Monteleone said.
Then, late Monday, the man called the Yellow Cab Co., claimed to be a police officer and told the dispatcher he needed a cab to pull over on Hempstead Turnpike because a woman was inside he needed to arrest, police said.
The cab did just that, stopping near Gardiners Avenue in Levittown.
There, police said, Mackrodt, carrying handcuffs and wearing a T-shirt with Nassau police insignia, displayed a weapon - later found to be a BB gun similar in appearance to a 9-mm semiautomatic handgun - and forced the 39-year-old Farmingdale woman into handcuffs and into the back of his 1989 Mercury sedan. Mackrodt did not explain why the woman was being detained, Caputo said.
She was released uninjured about three hours later, police said, when Mackrodt drove her to the Yellow Cab headquarters on Wolcott Road in Levittown and let her out.
Mackrodt, of 3 Brook Lane, took the handcuffs off the woman, then once again identified himself as a police officer and directed the dispatcher to give her a ride home, police said.
Police said the dispatcher, suspicious, noted Mackrodt's license plate, leading to a traffic stop early yesterday on Ridge Lane in Levittown, where the suspected impersonator was arrested. Police said Mackrodt was carrying a small shield similar to those carried by officers. He also had a laptop computer and the BB gun.
Mackrodt was charged with driving while intoxicated, kidnapping, criminal impersonation and multiple vehicle and traffic law violations. He is to be arraigned today at First District Court in Hempstead.
A Yellow Cab dispatcher who answered the phone declined to comment, citing the privacy of his company's passengers.
Staff writers Carl MacGowan and John Valenti contributed to this story.