In a televised national address on Monday evening, he announced a ban on private vehicle use, meaning anyone needing emergency medical care will need to ask a high-level district official for permission to leave their home.
Market traders selling food will also have to live close to their stalls for this period and cannot go back home.
Uganda has 33 confirmed cases of coronavirus, but officials say numbers will rise.
Patients, like pregnant women in labour, will have to first call an official before going out to seek medical help, unless they can access a government vehicle, which is often hard to come by.
BBC reports that there is a real sense of confusion following the president’s address, though officials are promising to clarify the new directives.
Strict rules on public gatherings are already being enforced. Schools have been closed and public transport banned.
President Museveni has promised food donations for people who have lost their income under the new restrictions.
But he has ordered the police to arrest politicians who offer food handouts to communities and for them to be charged with attempted murder.
In recent days, his opponents Bobi Wine and Kizza Besigye have been offering help to vulnerable Ugandans.