We have lost 13 children in this stampede and we have others in the hospital with injuries,” David Kabena, the police chief in the town of Kakamega, told reporters.
The crush took place at around 5:00 pm (1400 GMT) when panic broke out as the students went home for the day from Kakamega Primary school.
The reason for the panic is still unclear.
“We have launched an investigation to establish what exactly happened,” Kabena said.
Kenya Red Cross said on Twitter that emergency services were responding to a “fatal stampede” at the school.