The Russian-made Mi-171 came down while on a reconnaissance mission in Tamanrasset region, some 2,000km (1,200 miles) from the capital, Algiers.
The helicopter apparently experienced technical failure, but the exact cause of the crash is yet to be established, the ministry added.
Critics say Algeria has a poor aircraft safety record.
In 2014, 77 people were killed in a military plane crash.
Two military aircrafts collided during a training exercise in 2012, killing both pilots.
The reason for the helicopter's mission is not clear but militant Islamists are active in Algeria.
In 2014, Vietnam grounded its entire fleet of Mi-171 helicopters after a crash near the capital, Hanoi, killed 18 soldiers.
A military helicopter has crashed in southern Algeria, killing 12 soldiers, the defence ministry has said.