Anthony Kibuchi said authorities suspect that the person killed was carrying explosives, but police are still investigating.
The blast last evening happened near a military air base, and Kibuchi said authorities will try to determine if the base or military personnel were the intended target.
Downtown Nairobi has seen a series of grenade attacks over the last year, with one such attack killing nine people.
Al-Shabab militants in Somalia have threatened attacks in Kenya, but it's not clear that the small grenade attacks or Friday's blast are from al-Shabab, an al Qaeda-linked insurgent group.
Nairobi: A Kenyan police chief says a blast on a busy street in the capital, Nairobi, has killed at least one person.
First Published: Saturday, August 04, 2012, 13:28