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TV pictures showed a fire raging in a badly damaged building. A BBC reporter says 28 people have been taken to hospital with various injuries.
A Red Cross disaster response team has been sent to the scene of the explosion at a shopping complex on Moi Avenue.
Initial reports suggested an electrical fault might be to blame, but Prime Minister Raila Odinga has said the blast had a terrorist link.
“This is terrorism… this is a heinous act, we are under threat, but we will not be cowed,” he told reporters at the site of the blast.
There have also been reports of a man dropping off a bag at the site of the blast, minutes before the explosion.
Police commissioner Mathew Iteere had earlier said: “We are able to prove it was not a grenade attack or bomb attack… from the preliminary conclusions we do think it was an electrical fault,” he said.
But Kenya Power, the country’s sole electricity distributor, has said initial investigations had ruled out any electrical malfunction, reports say.
There have been several grenade and bomb blasts in Kenya since it sent troops into Somalia last year to tackle the al-Shabab Islamist militant group.
Al-Shabab has repeatedly threatened to stage revenge attacks against Kenya.
The BBC’s Kevin Mwachiro says glass and shoes and clothes from the small shops inside the building have been scattered across the street.
TV pictures have shown people pouring into the streets from nearby buildings to get away from the scene of the fire, the AP news agency reports.
Moi Avenue is a major road which would have been busy during the lunch hour, AP says.
According to an eyewitness, there was a huge blast and debris flew in different directions injuring people in the vicinity, the Nation newspaper reports.
The powerful explosion shook buildings in the surrounding area and the evacuation process began, the Nation says.