A further eight people remain in a critical condition after the attack on Lhubiriha secondary school in Mpondwe.
Boys who were staying in dormitories at the school are among the dead.
The Allied Democratic Forces (ADF) – a Ugandan group based in the Democratic Republic of Congo (DRC) – have been blamed for Friday’s attack.
Many of the bodies were transferred to Bwera Hospital, national police spokesperson Fred Enanga said.
The attack happened at around 23:30 local time (20:30 GMT) on Friday at the school in the Kasese district in western Uganda.
Over 60 people are educated at the school, most of whom live there
ADF rebels burnt a dormitory and a food store was also looted during the incident, Mr Enanga said.
Some of the boys were burnt or hacked to death, Major General Dick Olum from the Ugandan army told the media.
Others at the school, mostly girls, have been abducted by the group, he added.
Some of the bodies are said to have been badly burnt and DNA tests will need to be carried out to identify them.
The attackers are said to have torched the students’ mattresses and are also thought to have detonated bombs in the region.
Members of the wider community are possibly among the dead. A number of students remain unaccounted for.
Soldiers are pursuing ADF insurgents towards the DRC’s Virunga National park – Africa’s oldest and largest national park which is home to rare species, including mountain gorillas.
Militias including the ADF also use the vast expanse, which borders Uganda and Rwanda, as a hideout.
The attack on the school, located less than two kilometres (1.25 miles) from the DRC border, is the first such attack on a Ugandan school in 25 years.