Tanzania has not implemented any entry restrictions, but all arriving travelers are subject to medical screening upon arrival and the government is collecting tracking information for all international travelers.
Travelers and airline crew are subject to medical screening.
The Government of Tanzania is implementing temperature scanning for all international passengers arriving into Tanzania. Travelers who show symptoms of COVID-19 on arrival may be required to take a test. Travelers must complete a Health Surveillance Form on the plane and submit it to the Port Health authorities upon arrival.
Children under the age of 2 are exempt from presenting a COVID-19 test.
Travelers with proof of recovery from the virus within the last 90 days prior to boarding. Proof of a recent positive viral test and a letter from your healthcare provider or a public health official stating that you were cleared to travel.
More info at the CDC site
Travelers who did not get tested, are advised to stay home and self-quarantine for 10 days after travel.