"There was a blast here. Was it something that somebody was carrying? We will get to know once we have investigated properly."
At Nairobi's Kenyatta hospital, staff said 37 people were hurt, four critically.
Witnesses offered different account, some saying they saw a man blow up as he was running while others said a bomb had gone off in a dustbin.
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."
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.
Tribal and criminal violence traditionally flares before elections, and a presidential poll is due in December.
Separate bombs blamed on al-Qaeda killed more than 200 people at the US embassy in 1998, just a few blocks from Monday's blast, and 15 at an Israeli-owned hotel in Mombasa in 2002.