A Kenyan citizen who arrived in the country on Saturday from Congo via Uganda had been isolated and treated at Nairobi Hospital, Health Minister Aden Duale said on Tuesday.
The patient tested positive for the Ebola virus after developing symptoms associated with haemorrhagic fever.
The patient died late Monday while receiving treatment.
Health authorities have placed the country on high alert and are monitoring for possible additional cases.
Duale said 28 contacts, including family members and health workers who cared for the patients, had been identified.
Another 23 passengers who travelled on the same flight from Uganda were being traced.
The contacts will remain in isolation for 21 days and will be released after testing negative for the virus, the ministry's director, Patrick Amoth, said.
The patient will be buried within 24 hours in accordance with recommended public safety protocols.
Kenya is the fourth country to record an Ebola case in the current outbreak, which was declared in eastern Congo in mid-May.
Uganda recorded 20 cases and France one.
Before Kenya reported its case, there had been no active cases outside Congo since Uganda declared its outbreak over in late August.
This is the fastest-growing Ebola outbreak in history.
The World Health Organisation has warned it could become the deadliest as it continues to outpace efforts to track and contain it.
The outbreak is caused by the rare Bundibugyo virus, for which there is no approved vaccine or treatment.
Vaccine and treatment trials are under way in Congo's Ituri province, the outbreak's epicentre.
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