Goalpara is around 120 kilometres (75 miles) from the state capital of Guwahati. The police opened fire when members of the Rabha tribe, which is opposing the panchayat elections, started torching villages and attacked government officials. The police said they also attacked a Central Reserve Police Force (CRPF) jawan with a knife and tried to snatch arms from cops.
Four Army columns have been deployed, which is about 250 soldiers, on the request of the district administration, the Army said. It said four more columns are on standby.
The Rabha tribe wants autonomy in this part of the state and rejects government control. It believes that panchayats or village councils will undermine its own council's authority.
Violence has hit the area in recent days, with houses burned and roads blocked by cut down trees.
More than 10,000 people have lost their lives to unrest in Assam over the last two decades.