The trouble happened on Saturday night at a school in the west of the country, local media reports.
It began with a few students throwing stones and shouting "our rights", school principal Andrew Otara said.
It is the latest in a spate of arson incidents at Kenyan schools.
The pupils at the Itierio Boys Secondary School in Kisii were not allowed to stay up to watch the Euro 2016 match between Croatia and Portugal which kicked off at 22:00 local time (19:00 GMT), KTN television news reports.
There were also complaints that the state school had introduced new stricter discipline rules but the school has denied this.
Students set fire to seven of the school dormitories and tried to damage property at the neighbouring girls school.
Kisii County Governor James Ongwae wrote on his Facebook page on Saturday that "efforts by the disaster response teams and police to reach the place have been hampered by the unruly students".
He later said that the students caused "millions and millions and millions" of Kenyan shillings-worth of damage, adding that the ringleaders would be punished.
There has been fire damage at 20 schools in the area around Kisii in the last six months, Kenya's Standard newspaper reports.
Kenya's Education Minister Fred Matiang'i said that students from schools hit by arson attacks would only be allowed to transfer to other institutions with permission.
This was to stop future cases of arson and ensure they pay for the damage.
"Don't let the students who burnt schools escape paying for the damage because honestly it would be irresponsible for the government to continue spending billions of shillings repairing schools burnt by students, while they go scot free," Mr Matiang'i said.
Kenyan authorities are investigating if pupils who set fire to their school dormitories did so after being told they could not watch a Euro 2016 match on television.