The lawsuit, filed in state Supreme Court in Queens, claims the airline was "grossly negligent" in allowing Capt. Clayton Osbon to fly.
A flight attendant's ribs were bruised as passengers tried to restrain Osbon, but no one on board was seriously hurt. The March 27 flight was forced to make an emergency landing in Amarillo, Texas.
Osbon faces a hearing Friday morning in Amarillo to determine if he is mentally competent to stand trial. He faces federal charges of interfering with a flight crew. If convicted, he could be sentenced to up to 20 years in prison.
An airline spokesman did not immediately comment Wednesday on the lawsuit.
According to the lawsuit and a federal indictment, witnesses on Flight 191 say Osbon ran through the cabin in a wild rant. The first officer locked him out of the cockpit and passengers wrestled Osbon to the floor.
The lawsuit also claims he was "yelling about September 11th, Iraq, Iran, Afghanistan, al-Qaida and terrorists."
Other comments, according to the suit, included: "we're all going down", "you better start praying right now", "I'm going to show you Iraq and Iran right now", "there's a bomb on board" ''the plane will never make it to Vegas."
The lawsuit claims JetBlue knew or should have known he was unfit to be entrusted with the aircraft as pilot.
The 10 plaintiffs, all from the metropolitan New York area, are seeking unspecified damages for emotional distress.