An army detachment clashed with "an armed terrorist group", during an ambush on Saturday in the Gaadet Lahdjar area, in the prefecture of Ain Defla, killing corporal Mostafa Znanda, the ministry said in a statement.
Algerian authorities use the term "terrorist" to describe armed Islamists who have been active in the country since the early 1990s.
Security measures have been taken to seal and search the area and pursue the "criminals", the ministry added.
In May, the army announced it had killed two Islamists in the Ain Defla prefecture and seized weapons, ammunition and food products.
And in February, an Algerian soldier was killed in a car bomb attack in Timiaouine, in the south of the country on the border with Mali.
The army regularly announces the arrest or death of militants in different regions of the country.
In 2019, it said it had killed 15 armed Islamists and arrested 25 others, while another 44 had handed themselves in to authorities.
A civil war during the 1990s pitted Islamist militants against the Algerian government, leaving 200,000 people dead.
Despite a 2005 charter for peace and reconciliation designed to turn the page on the conflict, armed Islamist groups still remain active in some areas of the country, largely targeting security forces.
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