The latest attack is part of a sharp escalation in the region in recent months involving Palestinian militants, Israeli security forces and radical Jewish settlers.
It took place on Monday as Israeli forces were already on high alert and searching for a gunman who had killed two Israelis in the northern West Bank on Saturday.
Late on Sunday, Israeli settlers threw stones and firebombs at a Palestinian home south of Nablus near the site of Saturday's deadly attack, local officials reported, causing damage but no injuries.
Israeli security forces said in the latest attack the suspected Palestinian gunman opened fire at an Israeli car on the main north-south road in the West Bank, near the major city of Hebron. The army said the apparent drive-by shooting killed an Israeli woman and seriously wounded a man as the two were driving.
The Israeli rescue service reported the two victims were in their 40s and that a six-year-old girl who was also in the car was unharmed. The man, it said, was found semi-conscious and taken to the hospital.
Images from the scene showed the victims' car riddled with more than a dozen bullet holes. The gunman fled, prompting Israeli security forces to embark on their second manhunt in three days.
The Hamas militant group and Palestinian Islamic Jihad praised the attack as a response to Israel's expanding settlement enterprise in the West Bank, but stopped short of claiming responsibility.
The deadly shooting came just days after another Palestinian attack killed an Israeli father and son who were washing their car in the northern Palestinian town of Hawara, putting the West Bank on edge.
Nearly 180 Palestinians have been killed by Israeli fire in the West Bank since the start of this year, according to a tally by The Associated Press.
Israel says most of the Palestinians killed were militants. But stone throwing youths protesting the incursions and those not involved in the confrontations have also been killed.
Some 30 people have been killed by Palestinian attacks against Israelis during that time.
Israel says the raids are meant to dismantle militant networks and thwart future attacks.
Palestinians say the raids undermine their security forces, inspire more militancy and entrench Israeli control over lands they seek for a hoped-for future state. Israel captured the West Bank in the 1967 Mideast war, along with east Jerusalem and the Gaza Strip.
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