The woman died, officials said.
The woman was sitting on the left side of the plane when something in the engine apparently broke and smacked into the window. She hung out the hole for many minutes, said Amy Serafini and Hollie MacKay, who were in the seats behind the victim.
Many passengers kept trying to pull the woman back into the plane for a long time, until two men were able to get the woman back in her seat, they said.
A nurse answered a call for help and tried to do CPR.
Southwest CEO Gary Kelly said the family of the victim was the airline's primary concern.
"This is a sad day and our hearts go out to the family and the loved ones of the deceased customer," he said. "We will do all that we can to support them during this very difficult time."
The woman who was killed was identified as Jennifer Riordan, according to CNN affiliate KOAT, which cited Annunciation Catholic School. Riordan, 43, worked for Wells Fargo in Albuquerque, New Mexico, the station reported.
Terror in the cabin
"Everybody was going crazy, and yelling and screaming," passenger Marty Martinez said of the flight, which left New York and was forced to make an emergency landing in Philadelphia.
"As the plane is going down, I am literally purchasing internet just so I can get some kind of communication to the outside world," he said.
Passenger Matt Tranchin told CNN affiliate WPVI he was thinking, "That I'll never live to see my son born. That I'll never be able to say goodbye to my wife, say goodbye to parents. But I am. I am. I feel really very fortunate for that."
Tranchin told WPVI the crew was frantically trying to plug a hole left when a window shattered.
"Flight attendants rushed up. There was momentary chaos. Everyone kind of descended on where this hole was," he said.
The plane had suffered damage to one of its engines, and according to passenger Kristopher Johnson, who was sitting near the front of Flight 1380, debris from the engine flew into the window, breaking it and injuring a woman sitting nearby.

CNN