A vehicle belonging to Taita Taveta Woman Rep Lydia Haika knocked down and killed a pedestrian at Sultan Hamud on Tuesday night.
Police said the middle-aged man died on the spot.
The MP was travelling to Nairobi from Taita Taveta in the company of her daughter and driver. All the occupants escaped unhurt.
County police commander Joseph ole Napeiyan said the driver recorded a statement at Mukaa police station.
Ms Haika was unavailable for comment.