• The first case was reported on Friday, a 27-year-old woman who had travelled into the country from the US via London.
Health CS Mutahi Kagwe has confirmed another coronavirus case making the number to four.
"The latest case was confirmed today at our national influenza laboratory..the patient travelled from London, United Kingdom," Kagwe said on Tuesday.
"Tracing of persons who had been in contact with the person is ongoing."
Addressing the media, Kagwe said tests for two out of the 22 people who were quarantined last week turned positive.
"Confirmed cases are healthy, with no dangerous signs."
Kagwe said everyone coming into Kenya from a country affected by coronavirus must self-quarantine or risk being jailed.
"It is mandatory," he said.
Kagwe said they have so far tested 111 people in Kenya since the pandemic shook the world.
He said results of those at Mbagathi Hospital, 23 of them have tested negative and have been cleared to go home.
"36 contacts have been traced and are being monitored in relation to the two recent positive cases," he said.
"This is not a joke, this is the real disease. Nobody should imagine the threat facing us but let us be honest. We have four cases at the moment."
Kagwe said in order to mitigate economic loss, cargo vessels can come into the country so long as they are disinfectant at the point of dispatch and the crew guaranteed.
" There will be Kenya after coronavirus. For the UN headquarters, diplomats traveling to the UN, families and children can come in provided they also take measures," he said.
Over 6,000 people have died globally and thousands infected. The virus emanated from China's Wuhan province.
On Sunday, life began shutting down, literally, as the government moved in to limit the spread of coronavirus.