Maoists killed a policeman, who was part of a patrolling party on Friday.
The patrolling party was on its way to probe an attack by the rebels on an under construction paramilitary force camp in Bihar's Jamui District.
Additional Superintendent of Police Shafiul Haque said two others were injured in the incident. He added that they were admitted to the hospital and are out of danger.
The rebels, also known as Naxals, have fought for decades in a wide swathe of central and eastern India, including many resource-rich regions where tensions run high between poor farmers and industrial developers.
The Maoist insurgents are estimated to number between 6,000 and 8,000 hardcore fighters in nearly a third of India's 630 districts.
While they have made few inroads into cities, they have spread into rural pockets in 20 of 28 states.
Maoists say they are fighting for the rights of poor farmers and landless labourers. Thousands have been killed in the insurgency since the late 1960s.
Prime Minister Manmohan Singh has described the Maoist insurgency as India's biggest internal security challenge.
