Ahmad Shah Salim, police chief in the Nawa district of Helmand province, says the incident occurred today while the soldiers were on a regular patrol.
He says the soldiers' vehicle was destroyed in the explosion.
Roadside bombings are a major threat to both Afghan security forces and civilians.
Attacks using roadside bombs have escalated as the Taliban have intensified their campaign ahead of the US-led foreign forces withdrawal from Afghanistan in 2014.