The 46-year-old returned from Belgium on Monday aboard a RwandAir plane.
Tanzania on Monday confirmed its first case of Covid-19 in the country.
Health ministry said the 46-year-old woman returned from Belgium on Sunday aboard a RwandAir plane.
The woman was screened on arrival at Kilimanjaro International Airport (KIA) in Arusha but she did not have any symptoms of the virus. Later, she fell ill while in her hotel room in Arusha and went to hospital, Health Minister Ummy Mwalimu said.
Samples were taken to Dar es Salaam for testing and results confirmed the woman was infected with the coronavirus.
Ms Mwalimu added that the woman is in isolation and her condition is improving.
The minister urged Tanzanians to take precautions to prevent infection, and to report at any medical centre if they develop any symptoms of the disease.
The government suspended access social gatherings and ordered the closure of schools.
- Additional reporting by Emmanuel Onyango.