A senior policeman said: "We believe it is a suicide bomber.
"We are always peaceful. This sort of attack is very unusual for Nairobi."
Local KTN television said a man carrying a grenade was killed when it exploded as he tried to board a city bus.
One witness said: "We saw a person rushing towards a City Hoppa bus, then it was as if he changed his mind and rushed back."
"He was carrying a small carton. I think he was trying to run into the restaurant with the box but I saw it explode at the door. I saw about eight people lying on the ground."
Weeks of violence
Langat Justice, a 20-year-old student who witnessed the explosion, said: "It was a very loud explosion. I thought it was a tyre burst, but it was louder than that.
"Maybe this was a terror attack, we don't know," he said, as hundreds of people milled around and policemen tried to push them back from the scene.
Ali said the exact cause of the explosion was not yet known.
"There was a blast here. Was it something that somebody was carrying? We will get to know once we have investigated properly."
The blast came after weeks of violence by a criminal society called the Mungiki, which beheads its enemies.
At least 30 people were killed by police last week in raids on a Nairobi slum which is a stronghold of the gang.