At 1029 GMT, commercial banks quoted the shilling at 105.80/106.00 against the dollar, compared with 105.75/95 at Thursday's close.
The East African nation has 110 confirmed cases of the COVID-19 disease caused by the new coronavirus, which has also hit its crucial tourism and farm exports businesses.
The government has imposed a night-time curfew to curb the spread of the virus and traders said they were keenly watching to see if the government will order a lockdown.
"That's a factor making people buy (dollars)," said a senior trader from one commercial bank.