Passengers said they were met by authorities when the plane landed.
It took six hours before the passengers were able to get back on board and head to Los Angeles.
One passenger told Eyewitness News he smelled smoke and saw matches in a toilet of one the lavatories. Passenger Ryan Kelly said a man was acting strangely on board.
"The way I saw it, I don't think the guy was just trying to smoke a cigarette. It looked like he had some other agenda, some other plan. It looked very suspicious and all the aftermath with the FBI interrogating us. Seemed like more than just some guy trying to smoke on an airplane," said Kelly.
Passengers said it was a very long night, because they had to board the plane and then get off of it twice.
Another passenger told Eyewitness News a lot of people refused to get back on the plane to Los Angeles because the man's luggage was left on board.
"We were worried because they couldn't take his luggage off in Albuquerque because of the carousel type thing, which they couldn't handle there, so his luggage is here, which worried us a little bit," said passenger Julian Holloway.
The FBI said the man was not arrested and has been released from questioning.
It is not clear if he will be charged with a crime. The man's name has not been released.