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According to passengers and traffic controllers, the aircraft abruptly depressurized when a piece of an engine flew into it and broke a window.
A total of 143 passengers and five crew were reportedly aboard the Southwest's Boeing 737-700.
"One passenger, a woman, was partially … was drawn out towards the out of the plane … was pulled back in by other passengers", One passenger's father-in-law, relaying information from his daughter, said in a phone interview with NBC10.
Another passenger, Amanda Bourman, wrote on Instagram that one person died from a heart attack following the incident.
The flight reportedly took off from LaGuardia Airport in New York City and was heading to Dallas, Texas.
The left engine of the plane was said to have blown shortly after takeoff.
According to an altitude tracking tool on Flight Aware, the plane was flying around 32,500 feet when the incident happened. The plane descended by more than 3,000 feet per minute until the pilots leveled out around 10,000 feet.
Pieces of shrapnel flew into the plane's fuselage and at least one window, the passengers and the Federal Aviation Administration (FAA) said.