It was unclear how many of the victims were Burundian officers.
Major Felix Kulaigye from the Ugandan army said witnesses reported seeing the aircraft catch fire in the air before it crashed into Lake Victoria.
Ignatius Igundura, a spokesman for the civil aviation authority, said a rescue mission was under way.
"The rescue is on right now," he said.
The aeroplane was said to be carrying water purifiers, pipes and other equipment to be delivered to Ugandan peacekeepers in Somalia.
Uganda and Burundi are both involved in peace keeping operations in Somalia.
Vianny Lugya, an official from the Uganda civil Aviation authority, said the minister of transport would issue a statement.