Fourteen pupils died while at least 39 were seriously wounded in a stampede at Kakamega Primary School on Monday.
Western Region Police Commander Peris Kimani confirmed the report, saying 20 were treated at the county's general and referral hospital and discharged.
Reports indicated that the students were running out of class at 5pm when the tragedy occurred.
It was said that some fell from the third floor of the building.
Responders, including police and personnel from the Kenya Red Cross Society, went to the school to offer emergency services.
Leaders and security chiefs were among those who went to the hospital after receiving reports of the incident.
They included Kakamega Governor Wycliffe Oparanya, Lurambi Member of Parliament Titus Khamala and County Commissioner Pauline Dola.
Governor Oparanya visited the patients in their wards but left without addressing the media.
County head of communication Dickson Rayori said Mr Oparanya will address the media Tuesday morning.
Mr Khamala and Mumias East MP Benjamin Washiali called for thorough investigations into the tragedy by the ministry and the Directorate of Criminal Investigations (DCI).
Via Twitter, Deputy President William Ruto said: "We are devastated by the tragedy ... our prayers, love and thoughts to the families and relatives of the victims of the misfortune."
Also on the social media platform, Orange Democratic Movement leader Raila Odinga sent a condolence message in which he described the incident as "unfortunate and regrettable".
"I wish quick recovery to the injured children and pray that God grants strength to the affected families," he said.
He added: "There must be an immediate and thorough probe to get to the bottom of this incident."
Tragedies that have occurred in schools or affected students in the recent past include fatal accidents, deadly fires and the collapse of structures.
In September 2019, the Education ministry revoked the licences of two primary schools in Nairobi over safety concerns.
Education CS George Magoha closed Precious Talents Top School in Dagoretti and Pama Academy in Kangemi and ordered the affected pupils sent to public schools.
The institutions had substandard structures.
In January, three pupils died after lightning struck them at Mkulima Primary School in Kuresoi North Sub-County.
At least 53 others were admitted to various hospitals in Nakuru County.
Education officials partially closed the school and ordered the learners moved to the neighbouring Murinduko and Kerisoi primary schools, pending renovation of their classrooms.
In September 2017, nine students died while dozens others were injured after a fire burnt down a dormitory at Moi Girls' School Nairobi.
Parents accused the Ministry of Education of laxity in addressing such incidents.