More than 4,800 people have died and nearly 10,000 been infected in DR Congo since this outbreak began in May.
Only essential travellers, including aid workers, truck drivers and security personnel, will be allowed to cross the border from DR Congo to Uganda, subject to strict health screening, the health ministry announced.
Local youths reportedly accused the health workers of contaminating water sources and spreading Ebola.
The UN agency also extended its condolences to the family and colleagues of the nurse who was killed and wished the injured worker a swift recovery.
The Bundibugyo species of Ebola behind this outbreak is relatively rare and there is still no vaccine or specific treatment - though trials are under way.
The has contacted the Ebola response team for comment on the circumstances surrounding the attack in DR Congo.
Both tested positive for Ebola after travelling through Uganda, even though no cases have been reported there since August.
The World Health Organization (WHO) condemned the attack.
About 60 people who were being monitored after coming into contact with the Kenyan patient have all been discharged, it added.
In an attempt to prevent the virus spreading, neighbouring Uganda has banned all non-essential travel to and from DR Congo and says its citizens returning from there will be quarantined for 21 days.