The violence and the two-day shutdown come ahead of the second phase of assembly polls Dec 2.
The rebels Monday morning blew up a police jeep by detonating a landmine near Kasikewal in Chatra district, around 170 km from here. Three policemen were injured in the blast, an official said.
The injured were airlifted by helicopters and have been admitted to hospital.
In Khuti district, Maoist rebels blasted a bridge near Kasaribera village and blew up a school building at Sowde village. Rebels have blown up 10 school buildings this month. They are targeting schools as security forces are camping there for the elections.
On Sunday night, the rebels blew up the house of Rashtriya Janata Dal (RJD) block president Chandrika Yadav house in Johri village of Chatra district by using dynamites.
However, the RJD leader was not in the house when it was blown up.
The outlawed Communist Party of India-Maoist (CPI-Maoist) has called for a two-day strike beginning Sunday in Jharkhand, demanding that Maoist leader Ashok Mahto either be produced in court or before the media. Police, however, say Mahto has not been arrested.
Maoists claim he was held by the police two months back.
Maoist rebels have also asked people to boycott the staggered five-phased assembly polls that end Dec 18.
In the second phase of elections Dec 2, polling will be held in 14 assembly constituencies that are situated in Maoist strongholds.