"The home of the terrorist, who killed an Israeli baby and a young woman on October 22 in a tram station in Jerusalem, was destroyed in Silwan," an army statement said.
The home demolition came after two Palestinians armed with a gun and meat cleavers ran amok among worshippers in a Jerusalem synagogue on Tuesday, killing five of them, in the city's bloodiest attack in years.
Israeli Prime Minister Benjamin Netanyahu vowed a harsh response to the bloodshed, and pledged to speed up demolitions of the homes of perpetrators of attacks in Jerusalem in line with a policy announced earlier this month.
"This evening, I ordered the destruction of the homes of the Palestinians who carried out this massacre and to speed up the demolitions of those who carried out previous attacks," he said.
Home demolitions have long been used as a deterrent punishment in the occupied West Bank but it is the first time that they have been adopted as a matter of policy in annexed Arab east Jerusalem.
The Palestinian, whose home was destroyed, Abdelrahman Shaludi, was shot dead by police after his car rampage as he attempted to flee on foot.
The three-month-old baby he killed, Haya Zissel Braun, also had US citizenship. Karen Mosquera, 22, of Ecuador, died later of her injuries.
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