The current outbreak in DR Congo has been caused by the Bundibugyo species of Ebola, which is relatively rare, with no approved vaccine or treatment.
There are however four vaccines in development, with human trials for one of them launched in July.
Duale confirmed that the Kenyan national had tested positive for the Bundibugyo species.
According to the minister, the patient first travelled by road from DR Congo to the Ugandan capital, Kampala, where he boarded a flight to Nairobi.
Duale said that after being taken to the Nairobi Hospital, the patient was transferred to an isolation facility that was built during the Covid-19 pandemic.
It was there that the patient “developed fever, chills, intense fatigue and weakness, painful swallowing, muscle pain and bleeding under the skin”.
“Doctors suspected a viral haemorrhagic fever based on his symptoms and travel history and collected samples for testing. The sample tested positive for Ebola Bundibugyo virus,” Duale said.
The patient died at 23:30 (20:30 GMT) on Monday and his burial is planned for later on Tuesday in line with public health safety protocols.
At least 28 contacts, including family members and healthcare workers, have been identified, while health authorities are tracing a further 23 passengers and four crew members who travelled on the same flight.
A senior health ministry official said the patient might have passed screening at the airport because the medication he was taking masked his symptoms.
Kenya introduced tighter checks at airports and border posts after the outbreak was declared in DR Congo.
The health minister urged Kenyans “not to panic, as all systems are in place to mitigate the spread of the disease”.
He asked health workers to be “extra vigilant and maintain the highest infection prevention and control measures regardless of the condition being treated”.
