The bus crashed on Thursday night in the Kapchorwa District while carrying pupils back from an educational tour to Sipi Falls, the Uganda Police Force posted on X.
Survivors including three adults and several children were taken to several hospitals, according to police, who did not immediately give an exact number of people who were injured.
At least nine children were hospitalised in critical condition, while the adult who died appeared to be the founder and head of the school, Ugandan Minister of Local Government Balaam Barugahara Ateenyi said on X.
Residents of the village where the crash occurred acted as first responders and helped transport injured children to hospitals while trying to save some victims, Barugahara said.
The bus belonged to the King David Junior School, an elementary school in the capital Kampala, police said.
The driver reportedly lost control of the bus, which veered off the road, struck a rock and overturned, according to the police statement, which added that the information was preliminary and the cause of the crash was under investigation.
A police photo showed the bus lying on its side with the entire roof ripped off and the seats exposed, including some that were mangled.
Luggage and clothing lay strewn on the road.
Road accidents are common in Uganda and often are blamed on poorly maintained vehicles, speeding and poor road conditions, which are problems across Africa.
At least 14 people died when a bus collided with a truck in a remote area of northern Uganda earlier in July.
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