Police say the Maoists have not yet put forward any demands for his release.
Mr Singh was canvassing for the forthcoming state assembly elections. Polls are to be held in five phases between 27 November and 18 December.
Indian Prime Minister Manmohan Singh has described the Maoist insurgency as the single largest threat to the country.
The Maoists have a presence in more than 223 of India's 600-odd districts across 20 states, according to the government.
The rebels say they are fighting for communist rule and the rights of the poor peasants and landless. More than 6,000 people have died during the rebels' 20-year fight.
There has been a surge in Maoist violence in recent months - the rebels have kidnapped and killed policemen, help up an express train, attacked police stations, and blown up railway lines and communication links in affected states.
There have been more than 1,400 cases related to violence by Maoists between January and August, according to official records. Nearly 600 civilians have died in that period.