The Sovereign Council in charge of the country “decided to close all airports, land and sea border crossings, except to humanitarian aid,” spokesman Mohammad al-Fakki Suleiman told journalists.
State news agency Suna quoted a military spokesman as saying that cadets and trainees would be given leave as a precaution.
Sudan confirmed its first coronavirus case on 13 March. The man in his 50s died in the capital, Khartoum. He had arrived from the United Arab Emirates.
The country has stopped flights and bus trips to neighbouring Egypt to prevent the spread of the virus. Flights to China, Iran, Italy, Spain and Japan have also been cancelled.