Minister of State for Primary Health Care Joyce Moriku Kaducu said Wednesday that two of the new cases are Chinese nationals while the others are Ugandans.
Officials said one of the patients is an eight-month-old baby in Eastern Uganda, whose father travelled from Kenya recently.
Uganda reported its first case of the novel coronavirus (Covid-19) early this week.
On Saturday, President Yoweri Museveni announced that Uganda was closing all its border points to prevent people from crossing into the country in a bid to contain the spread of the coronavirus.
“Humans crossing into Uganda from the different border points are prohibited going forward. This is until we find coordination at the East African level. Please stay where you are. We are not against anyone but this is about manageability,” President Museveni said on Twitter.
On Tuesday, Mr Museveni said he is still assessing whether to ban public transport as part of his government’s efforts to prevent the spread of the coronavirus.
“Now, the only remaining thing is public transport. That’s what I’m still struggling with in my head. If you don’t have your private means of transport, don’t use public transport. Stay at home.
“Where are you going? I’m thinking of having temperature monitors at disembarkation and embarkation points of these public means of transport. I don’t want to ban them but I’m trying to discourage you (citizens) from using them,” Mr Museveni said while addressing the nation after Uganda’s first confirmed case of Covid-19.
“Before I came here, I saw a young man called Obuku who used to make a lot of noise speaking nonsense, but this time he spoke some sense. I heard him telling people to stay home. So coronavirus shouldn’t be underestimated because it’s making some people speak sense.”