But there is no functioning public ambulance system for medical evacuations, with many pregnant women, injured accident and crime victims and others relying on private means to get rushed to hospitals.
Ekwaro Obuku, a former head of Uganda's national association of physicians, told Reuters the order to pull private cars from the roads was likely to worsen an already-high maternal mortality rate.
"Other medical emergencies like maternal have not stopped because coronavirus has come," he said. "No mother in labour pains should ask for permission to deliver her baby. We will end up having unnecessary and preventable deaths." Some critics and rights activists have accused the government of relying on brute force to enforce anti-coronavirus measures.
"So we're going to have people dying en masse not from COVID-19 but rather from preventable deaths, preventable medical emergencies," said Adrian Jjuko, head of Human Rights Awareness and Promotion Forum.
Don Wanyama, the president's spokesman, did not respond immediately when Reuters sought comment.
Members of the police and the military were last week filmed beating up people, including women selling fruits in parts of the city centre, accusing them of defying orders to stay home.
The opposition has also warned that the urban poor might die of hunger if the government does not offer them food or some form of relief now that casual employment has fallen.
Museveni said anyone who attempts to distribute food to vulnerable people would be arrested because such activities would involve congregations that spread the virus.