The second patient, a 39-year-old man, is a close family member of the first case and was already in quarantine when he fell ill on Tuesday, the health ministry said in a statement.
It said he had been isolated immediately after developing symptoms including fever, fatigue and joint pains.
"Both cases are linked, and there is no evidence of spread in the wider community," the ministry said.
The second case will nevertheless add to worries in Kenya, the fourth country to register a case linked to the Ebola epidemic in DR Congo, the second-largest on record globally with about 9000 cases and more than 4000 deaths.
The first case emerged after a Kenyan man, who had been ill in DR Congo about a month before travelling by road to Uganda, flew to Nairobi on October 3, where a relative drove him to the hospital.
That case raised concerns about lapses in border screening systems in the region, with the patient able to cross the border between DR Congo and Uganda, which has been closed since May.
Kenyan authorities have located 113 out of 128 contacts of the first patient, with 108 people in quarantine.
"The other five are outside Kenya, and health authorities in those countries have been informed ... Tracing of the remaining 15 continues," the ministry said.
Authorities are also carrying out assessments of anyone in contact with the second patient since his symptoms emerged, including health workers and staff at the quarantine centre.
"This is the response working as designed," the ministry added, saying it would share updates on the patient's progress.
It urged Kenyans to stay calm but vigilant.
Ebola spreads through direct contact with the bodily fluids of infected people, whether living or dead.
The disease can cause fever, vomiting, diarrhoea and - in severe cases - internal and external bleeding.
Since the first case was detected last week, Kenya has set up a dedicated gate for screening passengers arriving from DR Congo and other countries potentially linked to the Ebola outbreak at Nairobi's Jomo Kenyatta International Airport.
Health experts say, however, that early symptoms can be hard to identify and medication including paracetamol can foil temperature checks, the traditional method used to screen passengers, along with health forms filled out by travellers.
The outbreak in DR Congo was declared in mid-May but may have started months earlier.
It is caused by the rare Bundibugyo strain of Ebola, for which there are currently no approved vaccines or treatments.
Uganda reported 20 cases and two deaths earlier in the year but was declared Ebola-free in August.
A doctor who returned to France in June from DR Congo tested positive but there was no further spread of the virus.
