The person lived in the Schwanheim district, which borders the airport, the city administration said.
Two new malaria cases in the neighbourhood had been reported on Tuesday.
The death brings the number of malaria-related fatalities linked to the airport this year to three, after two airport workers died from the disease in July and August.
Malaria is a potentially life-threatening mosquito-borne disease that is uncommon in Germany.
According to health authorities, so-called airport malaria occurs in "very rare" cases when an infected mosquito is brought into the country on an aircraft or in luggage, with transmission then taking place on the plane, at the airport or nearby.
Six airport workers contracted malaria tropica, the most dangerous form of the disease, in July after being infected by mosquitoes believed to have arrived on aircraft from malaria-endemic regions.
Two later died.
Health authorities in Frankfurt extended their condolences to the relatives of the latest victim on Thursday.
They said the two latest cases in the Schwanheim district were linked to an infected Anopheles mosquito that arrived in Germany by plane.
Both people contracted malaria tropica.
Neither of the two people had previously visited a malaria-endemic area.
They also did not work at the airport, it said.
Health authorities urged doctors to consider malaria in patients that come in with a fever.
Residents living near or working at the airport have also been urged to seek medical advice in case they display symptoms.
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