The victim has been identified as 43-year-old Jennifer Riordan, a Wells Fargo bank executive and mother of two from Albuquerque, New Mexico.
The plane, a twin-engine Boeing 737 bound from New York to Dallas with 149 people aboard, made an emergency landing in Philadelphia just before noon as passengers breathing through oxygen masks that dropped from the ceiling said their prayers and braced for impact.
National Transportation Safety Board chairman Robert Sumwalt said one person was killed. It was the first passenger fatality in an accident involving a U.S. airline since 2009, Sumwalt said.
A crew member on a plane reported to air traffic controllers that a piece of the plane was missing and "someone went out." In the audio recording of the exchange, the crew member says the plane needed to slow down.
It has not been confirmed that the person being referenced by the crew member is the individual who died.
Seven other people were treated for minor injuries, Philadelphia Fire Commissioner Adam Thiel said. He said there was a fuel leak in one of the engines when firefighters arrived and a small fire was quickly brought under control.
The Federal Aviation Administration said the crew reported damage to one of the engines, the fuselage and at least one window. The NTSB sent a team of investigators to Philadelphia.
Photos taken by passengers from inside the cabin and posted on social media showed what appeared to be significant damage to the jet, with part of the covering from its left engine ripped off and a window damaged.
Matt Tranchin was on his flight home from New York to his 8-month pregnant wife in Dallas when he saw an explosion ahead of him.
"Right around the time there was a huge explosion and glass shattering three rows ahead of me, that was about the moment that I realized this was not going to be a normal flight," Tranchin said.
Passenger Amanda Bourman told the Associated Press said she saw emergency medical workers using a defibrillator to help a woman who was taken off the plane after it landed.
The New York resident said she was seated near the back of the plane and was asleep when she heard a loud noise. She said the plane was fairly quiet because everyone was wearing an oxygen mask, while some passengers were in tears and others shouted words of encouragement.
Passenger Marty Martinez did a brief Facebook Live posting with the caption "Something is wrong with our plane! It appears we are going down! Emergency landing!! Southwest flight from NYC to Dallas!!"
John Goglia, a former NTSB member, told the AP that investigators will take the Southwest engine apart to understand what happened and will look at maintenance records for the engine.
"There's a ring around the engine that's meant to contain the engine pieces when this happens," Goglia said. "In this case it didn't. That's going to be a big focal point for the NTSB - why didn't (the ring) do its job?"
Goglia said the Boeing 737 is a safe plane but engine failures occur from time to time.
"We're pushing the engines to produce as much power as possible," he said. "We're right on the edge. Sometimes they fail, and that's why the containment ring is there."
The engine failure was reminiscent of a similar event on a Southwest Boeing 737-700 jet in August 2016 as it flew from New Orleans to Orlando, Florida. Shrapnel from the engine left a 5-by-16 inch hole just above the wing. Passenger oxygen masks dropped from the ceiling. Pilots landed the plane safely in Pensacola, Florida.
The Associated Press contributed to this report.