The centre said the first blast occurred on a 14-seater matatu, or public minibus, and the second was inside Gikomba Market, situated to the east of Nairobi's central business district.
The Kenyan Red Cross said five of its ambulances were evacuating casualties from the scene of the blasts.
The apparent bombings come amid a wave of attacks in both Nairobi and the port city of Mombasa, and come days after several countries issued new warnings about travelling in Kenya.
On Thursday and Friday, hundreds of British tourists were being evacuated from beach resorts near Mombasa because of the travel warnings.
Earlier this month three people were killed and 86 wounded in twin bus blasts in Nairobi that were blamed on Islamic militant cells linked to Somalia's Al-Qaeda-linked Shebab rebels.
Kenya has been targeted by the Shebab since sending troops to war-torn Somalia in 2011.
