Investigators say the window of Flight 957 broke as the plane was traveling from Chicago's Midway Airport.
Pictures posted to social media appeared to show a lengthy crack in one of the passenger windows on the jet.
Southwest didn't immediately release details on how the window was damaged. The crew never declared an emergency in the plane and the cabin did not depressurize.
A Southwest Airlines Co flight made an emergency landing in Cleveland at about 11 a.m. EDT (1500 GMT) on Wednesday after a window cracked in flight, airline officials and the Federal Aviation Administration said.
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King said there were no other mechanical problems with the plane, which was taken out of service. It was the first US airline passenger fatality since 2009.
The timing of the incident could hardly be worse for Dallas-based Southwest, the nation's fourth-biggest airline. Southwest estimates the drop in sales will cost it between $50 million and $100 million.
On April 17, a mid-air engine explosion on Southwest Flight 1380, another Boeing 737-700 from NY to Dallas, saw flying shrapnel shatter a window, partially sucking a 43-year-old banking executive out of the plane.
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