The Ministry of Health has sent a rapid response team to Ongata Rongai where the lady with coronavirus hails from.
"We have embarked on a contact tracing for all persons who have been in contact with her," CS Mutahi Kagwe said.
"We have sent a rapid response team to Ongata Rongai area where she lives for that purpose. There should be no panic."
Kagwe praised the woman for going to the hospital.
"I want to thank her because the minute she started feeling unwell she felt she needed to go to a hospital," he said.
"She is a very responsible citizen...She has given us the names of the people she has been in contact with."
The Kenyan Government has started tracking passengers on board flight which 27-year-old Kenyan woman confirmed to have coronavirus travelled in.
Kagwe said they are tracing passengers that were sitting next to the lady.
This new virus and disease were unknown before the outbreak began in Wuhan, China, in December 2019.
Coronaviruses are zoonotic, meaning they are transmitted between animals and humans.
The most common symptoms of COVID-19 are fever, tiredness and dry cough.
Some patients may have aches and pains, nasal congestion, runny nose, sore throat or diarrhoea. These symptoms are usually mild and begin gradually.
Some people become infected with the novel coronavirus but don’t develop any symptoms and don't feel unwell.
Most people (about 80 per cent) recover from the disease without needing special treatment.
Around one out of every six people who get COVID-19 becomes seriously ill and develops difficulty breathing.