Airports will remain open only for flights carrying medicine and equipment to fight the virus.
The ruling effects airports in Dili, Oecusse, Suai and Baucau.
The government ordered a state of emergency decree until April 28, declaring people must limit movement outside the home.
The closurecomes as authorities warned that the Nakroma passenger ferry between Dili and Oecusse could be a hot spot for virus contagion, urging people travelling on it to practice social distancing of one metre
On Monday, police inspector Carlos Zeronimo, said his officers were monitoring streets and businesses to ensure people were wearing protective masks and maintaining a one-metre physical distance from each other.
Authorities continue to urge people to practice social distancing of at least one metre, wash hands thoroughly and regularly and avoid touching their eyes, mouth and nose.
Symptoms of COVID-19 include difficulty breathing, fever and a dry cough.