Three women aged between 30 and 61 have tested positive for Covid-19, bringing the total tally in the country to 31.
Two of the women are from Kilifi County and are believed to have come into contact with Deputy Governor Gideon Saburi, who is in forced quarantine.
The third is from Nairobi and came into contact with a previously confirmed individual. The 31 cases are spread out in Nairobi, Kajiado, Mombasa, Kilifi and Kwale counties.
However, Dr Mercy Mwangangi, the Health ministry chief administrative secretary, expressed concern over the new cases coming from Kilifi.
"As we speak, there are consultations going on on how our teams are going to handle Kilifi and other areas that are emerging as hotspots. I, therefore, urge people at the Coast, and Kilifi in particular, to observe social-distancing with self-determination," she said.
Dr Mwangangi said 74 samples from suspected coronavirus cases have been tested at the National Influenza Centre, Kenya Medical Research Institute (Kemri), Nairobi, and Kemri-Welcome Trust Kilifi.
She said tracing of contacts is ongoing. "The new patients have already been taken into isolation in our facilities, and are being monitored by our medical personnel together with others who previously turned positive," Dr Mwangangi said.
The patients are aged between 20 and 67 and are currently isolated in various facilities.
So far, coronavirus infections in Kenya have taken the pattern of other countries, where numbers double in the second week, creating a fear that they could soar in the coming weeks.
Such a scenario would almost certainly overwhelm the health system. By the end of Friday last week, Kenya had registered seven cases since the coronavirus was first reported on March 13.
Since the crisis is projected to ravage the economy, on Wednesday President Uhuru Kenyatta announced a raft of measures meant to give Kenyans some relief.
The president reduced workers' income tax as well as value-added tax (VAT) and lowered the sales levy for small and mid-sized businesses.
The tax changes are aimed at lowering the cost of basic items while providing workers with additional income to boost consumption, which will in turn increase sales for traders, retailers and other outlets.
At the same time, Dr Mwangangi said there are more than 2,000 people who arrived into the country from Monday this week have been quarantined.
"Testing will be carried out after five days from the date of arrival. This is in line with the World Health Organisation (WHO) guidelines on testing," she said.
Forty-three countries in Africa have confirmed positive cases, with a total of 2,412. Fourteen countries have confirmed coronavirus deaths.
About a third of the cases are in South Africa, which recorded a steep rise overnight. Other countries with high numbers of cases are Algeria (264) and Egypt (402). The first case has been reported in Libya.
The WHO says adults aged 65 and above, and people of any age who have serious underlying medical conditions such as heart and lung disease or diabetes, might be at higher risk of coronavirus.
The global health agency says those that experience mild symptoms typically recover from the illness in about two weeks, while those who experience more severe symptoms could take up to six weeks.