"We suspect it is a grenade," a police officer at the scene told AFP. People at the scene said the explosive appeared to have been hurled at a bus stop and an adjacent food stall as people made their way home for the evening.
The attack comes a week after six people died when assailants burst into a church in Likoni district close to the port city of Mombasa and opened fire on worshippers.
The latest attacks come amid heightened warnings of a threat of Islamist violence in Kenya and despite boosted security in major cities.
Kenya has been hit by a series of attacks since sending troops into southern Somalia in October 2011 to battle Al-Qaeda-linked Shebab insurgents.