The Kenyan National Disaster Operation Centre said the first explosion occurred in a minibus and the second in the large open-air Gikomba market.
Uhuru Kenyatta, President of Kenya has vowed to fight the “evil” that terrorism represents 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.
Police officials said they suspect an improvised explosive device had caused the blast.
Hundreds of British tourists have been evacuated from the coastal resort area of Mombasa amid warnings of an attack.
British tour companies have also suspended flights to Mombasa, Kenya’s second largest city.
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