There was no immediate claim of responsibility but the explosion occurred in an area of far northeastern Kenya often targeted by the Somalia-based Islamist militant group Al-Shabab.
Interior Minister Kithure Kindiki said five people were killed and another five suffered "life-threatening injuries" in the blast caused by an improvised explosive device (IED) in the town of Elwak in Mandera County.
"The bomb unleashed by the criminals was laden on a donkey cart to avoid detection," he said in a statement.
"The crime scene has been sealed off for evacuation and investigations while various security formations are in pursuit of the attackers."
He did not say who was believed to be behind the bombing.
Kenya is a major contributor to an African Union force backing Somalia's fragile central government in its fight against Al-Shabab and has suffered a string of deadly retaliatory assaults.
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