Police said two improvised explosive devices had been detonated in the sprawling Gikomba market.
Meanwhile hundreds of UK tourists were evacuated from the coastal resort area of Mombasa amid warnings of an attack.
In recent years, Kenya has been hit by a spate of attacks, mostly been blamed on the al-Shabab militant Islamist group from neighboring Somalia.
The Kenyan National Disaster Operation Centre said the first explosion occurred in a minibus, the second in the large open-air Gikomba market.
Two people were reportedly arrested near the scene of the explosions.
Pictures from the scene showed clothing blown onto telephone wires above.
Fire engines and the Red Cross were at the scene tending the injured.
Kenyatta National Hospital in Nairobi said at least 70 people had been wounded.
“Many of the injured are bleeding profusely. We need a lot of blood,” a spokesman said.
President Uhuru Kenyatta vowed to fight “evil” terrorism following the attacks.
“All of us around the world must be united to ensure that we are able to fight this particular terror,” he said at a news conference.
Earlier this week, authorities tightened security at bus stations. They also ordered all vehicles to have clear glass windows.
Friday’s bombings took place two days after the UK, France and the US warned there was a high threat of attacks in Kenya.
Kenya had criticized the warnings, saying the tourism industry would be affected.
Correspondents say many Kenyans are expressing their frustration at the worsening insecurity.
The government recently rounded up refugees of Somali origin in an attempt to rid Nairobi of militants they believe to be hiding among refugees.
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