The demolition took place in Yatta, which is also the hometown of two Palestinian gunmen who killed four Israelis in Tel Aviv on Wednesday in the deadliest attack in a months-long wave of violence.
Israel freezes Ramazan permits for Palestinians after shooting
The murder in January of Dafna Meir, a 38-year-old nurse and mother of six, provoked fierce reaction among Israelis and prompted a personal vow from Prime Minister Benjamin Netanyahu that the assailant's house would be razed.
Israeli forces arrested 15-year-old Palestinian suspect Murad Ideis in a raid on his family home days after the attack.
Israel regularly demolishes the homes of alleged attackers in what it describes as a deterrent. Rights groups say it amounts to collective punishment, with families forced to suffer for the acts of relatives.
The army said Saturday's demolition was carried out without incident, adding that it had also made preparations for the destruction of the homes of both of the Tel Aviv gunmen.
That attack, which also wounded five bystanders, has prompted a range of measures from Israel, including a decision to temporarily bar entry for all Palestinians.
Three dead in Tel Aviv mass shooting
Violence since October has killed at least 207 Palestinians, 32 Israelis, two Americans, an Eritrean and a Sudanese.
Most of the Palestinians were carrying out knife, gun or car-ramming attacks, Israeli authorities say.
Others were killed in clashes with security forces or by Israeli air strikes in the Gaza Strip.
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