Nairobi police chief Moses Ombati said there would probably be more casualties after the explosion on the 25-seater bus.
“There are more casualties coming in but what I can confirm is that five people have been killed,” he said, adding that 10 men and three women were among the wounded.
Kenya Red Cross said 29 people had been wounded in the blast.
The force of the explosion tore apart the vehicle’s roof and seats and shattered the window of a nearby cafe. Two other cars were damaged.
A UN security official at the scene said the blast was caused by an improvised explosive device. Ball bearings could be seen, which could have wounded bystanders in the busy area, according to the official.
The attack took place in the Eastleigh suburb of Nairobi, sometimes referred to as “little Mogadishu” because of the number of Somali immigrants who live there.
Kenya has been hit by a string of grenade attacks recently, usually blamed on sympathizers of al-Shabaab, Somalia’s Islamist extremist rebels who are linked to al-Qaeda.
Al-Shabaab has vowed to carry out attacks on Kenya because it sent troops into Somalia last year to fight the rebels, who are considered a threat to Kenya’s security because they have been blamed for kidnapping foreign tourists and aid workers in Kenya.
African Union peacekeepers, led by Kenyan forces, drove al-Shabaab militants out of their last major urban stronghold of Kismayu in southern Somalia seven weeks ago.