The captain went to a toilet just outside the cockpit, and when he emerged began shouting "Iraq, al-Qaeda, terrorism, we're all going down!" according to the Amarillo Globe-News newspaper.
"It was a little scary. He was pretty freaked out," passenger Heidi Karg told a US network.
"When they were trying to calm him down... they had to restrain him and a bunch of male passengers ran to the front of the plane to subdue him."
The FBI is investigating the incident on Flight 191 from New York, which had 135 passengers on board, when the pilot-in-command decided to redirect the plane to Amarillo, Texas.
JetBlue said in a statement the flight was diverted due to a "medical situation" involving the captain, but made no mention of any commotion on board.
Al Jazeera's Bhanu Bhatnagar reports.