The rebels arrived in a truck, a minibus and on motorcycles early on Sunday to the police post at Sunwal in southwestern Nawalparasi district.
There, they exchanged fire with police for 30 minutes before detonating a bomb and fleeing, the country’s state radio said.
A further three offers are as yet unaccounted for.
The two dead civilians were named as Bhoj Raj Gopali, a streetside tea seller, and Ashok Nath Yadav, a government development worker.
Elsewhere, two guerrillas died in a separate firefight with the army at Sangram village in the Sarlahi district, located about 190 kilometres (118 miles) south of Kathmandu, an army official told AFP.
The Maoists fighters declared a “people’s war” in 1996, aimed at overthrowing the monarchy in an insurgency that has claimed more than 8200 lives.
The rebels on 27 August ended a seven-month ceasefire when the government refused to set up a special assembly to redraft the constitution.