According to a report on Reuters quoting Kenyan official, the blasts have allegedly killed at least four people and injured scores.
Earlier reports stated that the cause of the blasts is not known but Kenya has been hit by a spate of attacks in recent years.
They have mostly been blamed on the al-Shabab militant Islamist group from neighbouring Somalia.
Foreigners trying to leave Kenya after bomb warning
The Kenyan National Disaster Operation Centre said the first explosion occurred in a minibus, the second in the large open-air Gikomba market.
Police sources stated that they suspect the blast had been caused by an improvised explosive device.
The bombings took place two days after the UK, France and the US warned there was a high threat of attacks in Kenya.
It could be recalled that hundreds of British tourists were evacuated recently from the resort area of Mombasa amid warnings of an attack.
British tour companies have suspended flights to Mombasa, Kenya's second largest city.
Kenya had rebuked countries that issued warnings for their citizens.
Details of the tragic incident are still being expected.