Israeli forces were searching Palestinian homes in and around Hebron as well as setting up new checkpoints, an AFP reporter said.
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Media reports said a 16-year-old was seriously wounded and an 18-year-old was lightly hurt. The attacker managed to flee the scene.
Palestinian medics said the alleged assailant was 72-year-old Sharwat Sharawi, adding that she was driving in pouring rain at the time.
In the past two months, there have been near-daily Palestinian attacks on Israeli civilians and soldiers.
Mrs al-Sharawi’s death came as Palestinians launched more attacks on Israelis in a continuing wave of violence that intensified at the beginning of October.
Palestinian mourners chant Islamic slogans while carrying the body of fisherman Faris Meqdad, 18, during his funeral in Rafah, Gaza Strip, Friday, November 6, 2015. The hospital confirmed her age and said she had died before being admitted. At least nine Israelis have been killed in Palestinian attacks, a lot of them stabbings.
Also in Hebron, the Israeli military alleged that Palestinians fired at Jewish worshippers near a shrine in the city, wounding two people, aged 16 and 18.
In a separate attack, an Israeli man, aged 19, was seriously wounded near to the village of Beit Anon, south of Hebron, after allegedly being fired on by Palestinians, the military said.
Israel has accused Palestinian political and religious leaders of fomenting the violence.
Much of the violence has involved Palestinians attacking Israelis with knives, or ploughing into them with vehicles, and about half the Palestinians fatalities consist of attackers who have been shot dead.
But Obama is also likely to press Netanyahu on renewed peace efforts, though USA officials say the president has abandoned hopes of a comprehensive deal being reached before his second term ends in January 2017.
Earlier in the week, a 20-year-old Border Police officer was critically wounded in a suspected car-ramming attack near the location of the Friday Khalhoul incident.
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Israeli soldiers have responded with force, using live ammunition, rubber-coated steel bullets, tear gas and stun grenades. A Palestinian radio in Hebron has been shut down, and security against stone-throwers and crowds gathering has been stepped up.
