The clash occurred after Maoists attacked a team of the Royal Nepal Army's Thakurdwara Battalion which was trying to clear obstructions on the Kohalpur-Chisapani section of the East-West Highway, state-run Radio Nepal said.
A soldier was killed and two others were injured in the cross-firing, it said.
The Maoists have been blocking the road by cutting down trees and putting up other obstacles for the past two weeks.
In other incidents, two passengers were injured when Maoists indiscriminately fired at a passenger bus heading towards Kathmandu from Bardia at Mankhola area of Bardia district on Sunday, while two motorbike-borne Maoists shot dead a policeman at a traffic post in Balbari area of Morang.
