A ministry statement says that in addition to the 10 people who were killed, two were injured and two were missing.
The ministry did not immediately provide any cause for the crash.
Brunei's Sultan Hassanal Bolkiah visited two young armed forces cadets who survived the crash and expressed "great sadness."
Brunei's Borneo Bulletin newspaper called it "a national tragedy" that struck a day before the country's Muslim majority marked the start of the fasting month of Ramadan.