The attackers fled with the policemen's weapons, the report said.
An officer was among those killed, while two policemen were injured, the police said.
Jamui district magistrate Prem Singh Meena said police and paramilitary forces had cordoned off the area and were conducting search operations.
The Maoists have been active in Bihar's Jamui district, a hill area with a large tribal population, over the past couple of years. There have been several incidents of attacks on policemen and attempts to blow up railway tracks.
Maoist guerrillas, who are active in 13 of India's 29 states, say they are fighting for the rights of the landless, poor and tribal people and are inspired by the Chinese revolutionary leader Mao Zedong.
Federal Home Minister P Chidambaram recently told state security ministers that Maoist violence along with terrorism and insurgency in the north-eastern region were the three biggest challenges facing the country.
At least 562 people, including civilians, security forces personnel and rebels, have been killed in Maoist-related violence in India from January 1 to July 30, according to the government.