KLM spokesman Hugo Baas said the passenger was handcuffed by the captain and guarded by two passengers for the rest of the flight.
He said everyone on board was shocked, but no one was injured.
The 28-year-old Dutchman, whom Mr Baas described as clearly unstable, ignored orders from flight crew to turn off his mobile phone, ripped up his passport and said he would hit passengers and flight attendants.
He then sat in business class, claiming he suffered from claustrophobia.
Mr Baas said: "So at 37,000 feet he decided it was time to go and tried to open the emergency exit."
Due to the cabin pressure, it was impossible to open the aircraft's emergency door.
On arrival at Newark, New Jersey, the man was put on the next flight back to Holland under the supervision of two private security agents.
He was arrested at Amsterdam's Schiphol Airport and will face charges of attempting to endanger the lives of passengers.