The two patients are foreign nationals from the US and Germany.
Tanzania has reported two new coronavirus cases raising the total to three, Prime Minister Kassim Majaliwa has confirmed.
Majaliwa on Wednesday told journalists that the two patients are foreign nationals from the US and Germany.
One case was confirmed in Dar es Salaam and one in Zanzibar, according to Majaliwa.
Tanzania confirmed its first case of the coronavirus pandemic on Monday in the northern town of Arusha.
The patient, a 46-year-old Tanzanian woman, had 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.