An army patrol vehicle early this week hit a homemade landmine near the southwestern village of Tingara, the defence ministry said in a bulletin.
Other soldiers were also wounded and taken to hospital, it added.
Niger is ruled by military leaders who seized power in a July coup, citing a worsening security situation as justification for the power grab.
But jihadist violence that had already gone on for eight years has continued.
The patrol was heading back from Inates in the western region of Tillaberi, which is prone to jihadist attacks.
The army said it later carried out an air strike after tracking those it said were responsible and "neutralised" several of them.
Another air strike targeted "a group of terrorists" in Amalaoulaou in Mali, killing at least eight fighters and destroying equipment, it said
Last month, 23 Nigerien soldiers died in a "terrorist" ambush in Tillaberi, which borders Burkina Faso and Mali, both also under military regimes.
The Niamey regime also faces violence by Boko Haram jihadists and their rivals Islamic State West Africa Province (ISWAP) from the southeastern region of Diffa near Nigeria.
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