Thirty-four others were injured and taken to Mwingi District Hospital where four, including a pregnant woman, were admitted.
The bus christened ‘Dalsan’ was destined to Mandera on Monday, when the driver lost control.
The accident comes barely days after scores of people died in similar incidents.
Last month, 23 people, most of them members of one family, died in a road accident in Mbooni East District while returning home after visiting their in-laws in Makueni.
The minibus plunged into a dry riverbed as they crossed Uaani Bridge along the Wote-Machakos highway.
Eleven men, 11 women and a child died in the accident. Thirty-four other passengers were seriously injured and admitted to Machakos District Hospital in serious conditions.
In other recent road accidents across the country, 11 people died in Voi, eight in Isiolo, 13 in Machakos, four in Homa Bay, 20 in Meru and five in Bomet.
Vice President Kalonzo Musyoka flew to the scene in Mwingi and later visited the injured at the hospital.
He was accompanied by Defence Assistant Minister David Musila and Kitui South MP Isaac Muoki.
Mandera MP Mohammed Hussein Ali also joined them later.
The driver of the fatal bus fled after the accident and could not be traced. Police said they were looking for him as they launched investigations into the incident.
Mwingi Central DC Peter Kinuthia and OCPD Peter Kimani, who rushed to the scene, confirmed that six men, four women and three children perished on the spot during the accident.
Most of the survivors were still in shock and could not speak to the media.
Adan Weye, Mohammed Abdi and Ali Dubane said they could not recall how the accident happened since the bus was “not speeding”.
“I only thank God that I survived the accident. I do not know how and what happened before the crash. I cannot recollect anything,” Adan told The Standard at the scene of the crush. The VP told the police to ensure that traffic rules were strictly observed to stop further deaths on the road.
Kalonzo said most accidents were caused by human errors, specifically, drivers being careless. He said Michuki rules must be reintroduced on the roads to stem increasing accidents.
The 13 passengers who died in the accident were last evening buried at Mwingi Cemetery, according to Muslim rules.
A 2009 UK transport report ranked Kenya as the fifth country in the world, among 29 others sampled, with the highest number of accidents per licensed vehicles.
The report, however, put Kenya the highest in Africa. The report noted that road safety trends in the country were worse, especially after the reluctance of “Michuki rules”.