The Dallas County Health and Human Services first reported the death in the news release Sunday.
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The woman was in her 30s and had "underlying high risk health conditions," Dallas County said in a news release.
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She was reportedly on a Spirit Airlines flight July 24 when she became unresponsive, spokeswoman for Albuquerque International Sunport Stephanie Kitts told CNN.
The plane was immediately diverted to Albuquerque, Spirit Airlines told CNN in an email.
"The proper authorities responded and it was determined that the individual was deceased on arrival," Kitts said.
Dallas County officials initially provided an incorrect location of the plane at the time of the woman's death.
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Because there was no mention of COVID-19 at the time the flight was diverted, airport officials treated this as they would any other medical incident, Kitts said.
Spirit Airlines said its crews are trained and equipped to deal with passengers' medical problems during flights.
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"Our Flight Attendants have in-depth training to respond to medical emergencies and utilize several resources, including communicating with our designated on-call medical professionals on the ground, using onboard medical kits and personal protective equipment, and receiving assistance from credentialed medical personnel traveling on the flight," spokesman for Spirit Airlines Erik Hofmeyer said in an email statement to CNN.
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Spirit has "enhanced cleaning protocols," on board its aircraft, and its air filters "capture 99.97% of particles and filters the air for contaminants every 2-3 minutes," Hofmeyer said.
Even though the woman's death happened in July, it was included in the 554 confirmed new COVID-19 cases reported by Dallas County on Sunday. More than 8.2 million cases have been reported nationwide as of Tuesday afternoon, according to Johns Hopkins University data, and more than 220,000 have died.
The news comes as people appear to be getting more comfortable flying during the pandemic: The Transportation Security Administration screened more than 1 million passengers Sunday, according to the agency, the most since March 16.
While some studies, including two published last month, have suggested the coronavirus can spread on airplanes, a Department of Defense study released last week showed that airplanes' ventilation systems filter the air efficiently and take out particles that could transmit viruses.
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