Police said in a statement that six others who were found in critical condition have been admitted to the hospital, but could not state the cause of the fire at Salama School for the Blind, according to the Associated Press (AP).
Fatuma Ndisaba, a top official in Mukono, told local broadcaster NTV that the victims, including children aged between 7 and 10, were burned beyond recognition.
With the support of families, she said, the victims' bodies will be identified through DNA investigations.
"I have no words to describe the pain I am going through," Richard Muhimba, the father of a dead child who lives in the nearby town of Mukono, told AFP.
"I visited him on Saturday, he was in good health, and three days later he died," he said on the phone before hanging up, overcome with grief.
The Salama School for the Blind, built in 1999, has dozens of students, aged between 6 and 25.
Fire incidents at schools have been a cause of concern for education officials in the East African country where classrooms and dormitories are often crowded.
There's usually no firefighting equipment in place, and officials sometimes blame incidents on poor electrical connections.
RHM/PR