At least five other soldiers were injured in the battle in Aurangabad district late on Monday.
Maoist rebels have carved out strongholds in a number of states in the north, east and centre of India.
They say they are fighting for communist rule and greater rights for tribal people and the rural poor.
Three rebels were also killed in Monday night’s gunfight in the Dumrinala area, nearly 170km (105 miles) south of Patna, the capital of Bihar, police officer PK Sahu told the Associated Press news agency,
The police said the rebels used improvised explosive devices and fired at the soldiers when the latter were conducting anti-rebel operations in the area.
India’s Maoist insurgency began in West Bengal state in the late 1960s and has been called the country’s “greatest internal security challenge”.
The Maoists control large areas of several states in a “red corridor” stretching from the north-east to central India.