The vehicle, known as a matatu, was travelling from Sirare on the Tanzanian border to the port city of Kisumu when the accident took place.
"Officers collected eight bodies at the scene. Unfortunately three others passed on while being rushed to the hospital," said traffic official Andrew Naibei.
Local police commissioner Mohammed Maalim said the minibus was carrying too many passengers "and we expect a thorough investigation (into) how such an overloaded matatu could travel all the way from Sirare," he said.
But the World Health Organization (WHO) believes the figure could be as high as 12,000.
In December a tanker carrying flammable materials ploughed into 11 vehicles, causing a fireball that left over 40 dead.
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