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
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.