Ebola virus disease is a severe illness that is spread through contact with the body fluids such as vomit, blood and faeces of a person sick with the disease.
The World Health Organisation's emergency committee will meet on Friday to decide whether the outbreak constitutes an worldwide emergency.
All of the boy's family members are in isolation, Aceng said, with two case-contacts showing symptoms of Ebola.
"Congolese health authorities immediately notified the Ugandan authorities and provided them with the names and phone numbers of suspected cases", the DRC health ministry said.
Despite the fact that Rwanda is surrounded by this public health threat, no Ebola case has been reported in the country, the ministry of health said in a public notice.
The announcement of the first cross-border case puts new pressure on WHO to declare the Ebola outbreak a global health emergency.
The Ugandan cases show the epidemic is entering a "truly frightening" phase and could kill many more people, one infectious disease specialist told Reuters. 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.
They have been isolated at a hospital near the Congo border. "She does not have to go through the official border points", Mwebesa said from Kasese, a district near the border where the family was being treated.
"The current cases in Uganda will be quickly contained but the failure to stop the current Ebola epidemic in DRC is simply tragic", said Ian Jones, a professor virology at Britain's Reading University.
Ongoing work to strengthen national capacity for early detection and containment, it added, include robust community awareness and mobilisation, logistics, an EVD treatment centre, and surveillance. Congo has been experiencing an outbreak since last summer.
"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.
"We can expect and should plan for more cases in (Congo) and neighboring countries", warned Dr. Jeremy Farrar with the Wellcome Trust, which is funding vaccine research in this outbreak. Roughly 4,700 health workers in 165 health facilities have been vaccinated.
The outbreak is the 10th in the DRC since the disease was identified in 1976.
Unlike the outbreak in West Africa that killed more than 11,000 people, there are now vaccines and experimental treatments to help stop the spread of the disease.
Uganda accepts refugees from Congo, and many health workers felt that despite their best efforts, spread of the virus to Uganda had just been a matter of time.