Some reports say she received oxygen before she died.
Stephanie Kitts, a spokeswoman for Albuquerque International Sunport, said in an email to The Arizona Republic, there was no mention of Covid-19 at the time the flight was diverted to that airport, so the incident was treated like any other medical event.
The Washington Post reports that Spirit Airlines alerted the US Centers for Disease Control once they learnt that the woman had died of Covid-19 on one of the airline's flights.
Spirit Airlines' spokesman Erik Hofmeyer added that the airline was never asked to share passenger manifests so close contacts could be tracked down.
The CDC says it has no record of being contacted by the airline.
Passengers on that flight in July only heard about the woman's death being related to Covid-19 in October, when media in the US found out which flight the woman had been on.
State health officials in New Mexico have reportedly admitted that they failed to investigate the incident.
The results of the woman's autopsy were only revealed in late September.
It is not known whether the woman realised she had Covid-19.