As the man exited, some gasoline spilled on the floor.
The security officer then notified two police officers outside the cathedral, who caught up to the man and began to question him. While he was cooperative, his answers were inconsistent and evasive, Miller told the media.
"His basic story was that he was cutting through the cathedral to get to Madison Avenue, that his car had run out of gas," Miller said. "We took a look at the vehicle. It was not out of gas, and at that point he was taken into custody."
The man was also carrying two bottles of lighter fluid and two extended butane lighters, he added.
Charges were not immediately filed against the man, whose name the police did not release. "He is known to police," Miller said, without elaborating.
The incident comes two days after a devastating blaze ripped through the Notre-Dame Cathedral in Paris, one of that city's most famous monuments. Investigators are still looking into the specific cause of that fire, though it was believed to be accidental.
St. Patrick's Cathedral seats about 2,200 people and opened its doors in May 1879.