Thursday's protest by motorbike taxi riders was sparked off by the arrest of one of their colleagues for not obeying restrictions aimed at curbing the spread of the coronavirus.
According to a statement by the police, the offender was being escorted to a police station when a row erupted with other motorbike riders, leading to one being shot dead on the spot.
Two more protesters died after shots were fired at them as they attacked a police compound in the area.
Kenya's Inspector General of Police has since ordered the arrested officer involved in the shootings to be suspended as investigations got underway over the incident.
Members of the Kenyan public have accused the police of using deadly force to put down protests against restrictive measures in force to tackle Covid-19.
Earlier this week, 13-year-old Yasin Moyo died after being shot while watching from a balcony as the police cleared the street below of people amidst a night curfew.
Duncan Ndiema, the officer accused of his killing has appeared in court but pleaded not guilty to the charge.