The incident aboard Flight 546 occurred about 20 minutes after the plane had left Houston bound for Chicago with 160 passengers, the Houston Chronicle reported.
Witnesses told authorities the man, identified as a 34-year-old from Burbank, Ill., made his way to the front of the cabin and said he had to get off the aircraft.
Passenger Sara Olkon said people screamed as men rushed toward the man.
"It was the sound of terror," she said.
FAA spokesman Lynn Lunsford said the passenger tried to open a pressurized door, which is not easily accomplished.
But the incident caused the pilot to contact air traffic controllers at 1:15 p.m. and the Boeing 737 was diverted to Lambert-St. Louis International Airport where it landed safely at 1:25 p.m., Lunsford said.
Two passengers and a crew member held the man to the floor until law enforcement officers arrived and took him into custody for questioning, the Chronicle said.
He had yet to be charged by late Sunday.
Continental spokeswoman Julie King said there was no indication the man had terroristic intentions.
The rest of the passengers made their way to Chicago by 3:24 p.m.
The incident was the second instance of a plane being diverted Sunday. A Delta Air Lines flight from Detroit to San Diego was diverted to New Mexico when a threatening note was found in the plane's bathroom, The Detroit News reported.
Flight 1706 bound for San Diego landed at Albuquerque International Sunport Airport and taxied to a secure area.