The spokesman for Afghanistan's defence ministry, Gen Mohammad Zahir Azimi, said the powerful blast hit the soldiers' vehicle today in the Dilaram district of Farah province.
Azimi said no other soldiers were seriously wounded, but declined to provide further details on the explosion.
There was no immediate claim of responsibility.
The Taliban have escalated attacks in recent months as they try to take advantage of the withdrawal of foreign troops, who handed over security for the country to Afghan forces over the summer.
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