The woman who was being quarantined in the western city of Nakuru has taken her own life.
Health workers found her dead at the Kenya Industrial Training Institute facility where she was being held, having apparently hung herself, local media say.
Local government officials also state that initial police investigations are “pointing to suicide”.
The woman was said to be in her 20s.
Nakuru county officials confirmed she arrived in Kenya from South Africa on Wednesday. They are not naming her until they have contacted her next of kin.
Local media quote unnamed sources as saying the woman had recently complained she was being held in “deplorable conditions” and had asked to be transferred elsewhere.
Many countries have imposed travel restrictions, plus mandatory quarantine for any new arrivals to curb the spread of coronavirus. Kenya’s quarantine period lasts for 14 days.
Currently Kenya has confirmed 31 coronavirus cases, one of whom died.
Meanwhile South Africa has the highest number on the continent – at more than 1,000.