In November 2018, Uganda vaccinated its health workers against Ebola despite there being no outbreak of the disease in the country. Another suspect, a resident of Kyarumba Sub County, who was not in contact with the family has also been admitted.
People are infected when they have direct contact through broken skin, or the mouth and nose, with the blood, vomit, faeces or bodily fluids of someone with Ebola.
The news will likely to increase pressure on the World Health Organization (WHO) to declare the outbreak a public health emergency of worldwide concern.
"All the other Congolese family members have been identified and are in isolation at Bwera hospital", said a spokesperson for the ministry, speaking on national television.
The new patients are in western Uganda's Kasese District, across the border from hotspots in the DRC's Ebola outbreak.
A WHO expert committee has been put on alert for a possible meeting on whether to declare a global health emergency in light of the cross-border cases.
"The boy who tested positive for Ebola in Kasese yesterday passed on last night in the isolation unit", the official told AFP on condition of anonymity. More than 2,000 cases have been recorded since the start of the outbreak, the DRC's 10th to date, and almost 1,400 people have died.
The family returned to Uganda with four other family members of Congolese origin, Aceng said.
In preparation for a possible outbreak, Uganda has vaccinated almost 4,700 health workers in 165 health facilities.
The boy is now receiving treatment, and people he came into contact with are being monitored, the World Health Organization said.
The outbreak in Uganda comes in the wake of a deadly outbreak in DR Congo's provinces North Kivu and Ituri, which has persisted for10 months.
"A step up in the national response with full global support is critical if we're to contain the epidemic and ensure the very best protection for the communities at risk and for the health workers working to protect lives", Farrar said.
"There are now more deaths than any other Ebola outbreak in history, bar the West Africa Epidemic of 2013-16, and there can be no doubt that the situation could escalate towards those awful levels".
Violence and mistrust hamper containment efforts there, as treatment centers are often attacked by militia groups, and people are either too scared or too suspicious to seek medical help, CBS News' Debora Patta reported. Millions of travellers along Congo's border with Uganda and Rwanda have been screened for Ebola since the outbreak began.
Uganda's health experts are also asking people who live along the DRC-Uganda border to take a number of preventive steps, from washing their hands thoroughly to avoiding "social norms like shaking hands and hugging".