The company issued a statement on Twitter saying "We have lost bulk power supply to various parts of the country due to a system disturbance," but said it was working to "restore normalcy within shortest time possible."
Kenya Power did not provide specifics as to what caused the problem in its grid.
The outages follow widespread blackouts this month in East Africa's economic powerhouse.
In January a high voltage transmission line connecting the capital broke, causing a nationwide blackout.
Later that month, three senior managers Kenya Power were charged with sabotage and negligence.