Air Tanzania said it was temporarily suspending flights from Dar es Salaam to Moscow from Friday.
The airline said on Facebook that it took the step after "a routine risk assessment of the operating environment along the route."
Passengers with tickets will be offered a full refund, the airline noted.
"We continue to monitor conditions in consultation with the relevant authorities and will announce the resumption of services as soon as the assessment supports it," the statement read.
While the airline's official statement did not explicitly mention safety in Russia, or the Ukraine-Russia War, the announcement makes it the first airline to suspend flights after Ukrainian President Volodymyr Zelensky warned this week that the skies over Russia were unsafe.
Russia says no foreign airlines plan to stop flight to Russia
Russian aviation watchdog Rosaviatsiya stated on Thursday that it had not received any withdrawal notifications from any foreign airlines, Interfax news agency reported, citing the agency's head, Dmitriy Yadrov.
He said that the Russian foreign ministry and the watchdog would cooperate with the International Civil Aviation Organisation (ICAO) on civilian flights to and from Russia after Zelensky's warning.
"They work very closely with us and understand all our rules, standards and how we ensure flight safety," Russian news agency Interfax quoted Transport Minister Andrei Nikitin as saying.
He said that the ministry gave the clarifications in response to requests from foreign carriers.
While European and US carriers have avoided Russian airspace since the start of the Ukraine war in 2022, airlines from China, Turkey and Gulf states still use it.