The government closed schools and asked people to work from home where possible last month, after the East African nation reported its first case of the virus.
Confirmed cases have risen to 208 and additional restrictions, including a night time curfew, have been imposed.
Safaricom, which is partly owned by South Africa’s Vodacom and Britain’s Vodafone, said mobile phone data usage had jumped 35% as users streamed movies, worked from home and used social media sites like Facebook.
The company is one of the biggest providers of internet access in Kenya, supplying 300,000 homes with a fibre connection, and nearly all of the 47 million population with second, third and fourth generation mobile internet coverage.
Along with financial services platform M-Pesa, the data business has been one of the key drivers of earnings growth for Safaricom in recent years.