CEO Peter Ndegwa says all staff at the branch being counselled and screened for the virus.
Telco giant Safaricom has closed its Thika Road Mall (TRM) shop after a staff tested positive for the coronavirus.
The store will be temporarily closed for cleaning and sanitisation.
Safaricom CEO Peter Ndegwa said they were notified of the test results on Sunday morning.
"The employee is currently in isolation and receiving appropriate medical attention," he said in a statement.
He added that the company’s top most priority was the health, safety and wellbeing of the staff.
All the other staff who were working at the branch have been informed of the development and are currently being counselled and screened.
"We are fully supporting our affected colleagues and their families, through the recovery period by providing all necessary medical care and psychosocial support required, ensuring their wellbeing," the telco chief said.
Meanwhile, the affected customers have been encouraged to access services from nearby shops and through self-service channels.
"Even as we take these actions, we reiterate our commitment to continue working with all stakeholders to help our nation through this crisis," Ndegwa added.
Kenya on Saturday confirmed 143 new cases of the virus to take its infection tally to 1,888, 79 days after the first case of a woman who travelled from the US via London was reported.
The Safaricom staff was part of the 143 new cases.
Of the new cases, 86 cases were in Nairobi with 45 from Makadara while 21 were from Kibra. Embakasi South come third with six cases. Langata had one case.
Uasin Gishu reported 11 cases, all truck drivers.
The disease has spread to 33 counties, the latest being Kericho which reported one case in Ainamoi area.