According to the Authority, the students were from a school in Tharaka Nithi.
In a statement, NTSA said the driver of the matatu escaped, but efforts are underway to apprehend him.
The authority said following the incident, the vehicle was towed to a police station for further action.
"Alternative transport arrangements were made for the learners," NTSA said.
"Drivers and school management entrusted with the safety of our children must understand their responsibility."
From March 27, NTSA has mounted compliance checks on major highways, catching most motorists unawares.
The multiagency team comprising officers from the NTSA and National Police Service have been erecting roadblocks, in efforts to ensure compliance by the sector players.
On Friday, the National Transport and Safety Authority suspended the operator licenses for two saccos.
"The Saccos failed to comply with provisions of section 5 of the NTSA (operation of PSV) regulations, 2014 and analysis of sped data violations that were compiled through the NTSA intelligent road safety
management system," they said.
The authority directed the saccos to comply with all the requirements of the Traffic Act and the PSV regulations.
The authority also directed the Saccos to present all the vehicles in their fleets for inspection.
It further said all the drivers of both saccos are to undergo road safety sensitisation.