The accident comes days after a Pwani University bus got involved in a road accident which has so far claimed 17 lives.
The accident which occurred on Thursday has been linked to the failed brakes.
16 people died as a result of the accident.
Over 60 people were seriously injured and taken to Naivasha sub-county hospital before some were later transferred to Nakuru for specialised treatment.
Following the accident, learning at the university has been suspended.
In a memo by Vice Chancellor Mohamed Rajab, learning will resume on Monday.
The accident occurred after the bus that was heading to Nakuru from Nairobi developed some mechanical breakdown before hitting the matatu that was also headed in the same direction.
Both vehicles landed in a ditch trapping the occupants before members of the public came to their rescue while others died at the scene.
According to Naivasha OCPD Samuel Waweru, the full bus, was ferrying the students to Eldoret for college games when the accident occurred.
He said initial investigations indicated that the bus brakes system failed and in the process, the bus hit the Nissan matatu that had 14 passengers.
I learned of my son's death on social media- Hilary Litali's dad