Such demolitions, heavily criticised by rights groups, have regularly resulted in clashes between Israeli security forces and Palestinians.
The home set to be demolished is located in the Shuafat refugee camp and was the residence of Ibrahim al-Akari, who carried out a car-ramming attack on November 5, 2014, killing two people, including a border police officer, police spokeswoman Luba Samri said.
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The 38-year-old drove his van into a group of police officers before ramming into pedestrians at a tram stop along a road separating east and west Jerusalem.
He then jumped out of his vehicle and attacked bystanders with an iron bar before being shot dead by police.
Israel says such demolitions act as a deterrent to potential attackers, while rights groups and Palestinians say it amounts to collective punishment, forcing family members to suffer for acts committed by someone else.