The incidents extended a five-week-old campaign of Palestinian attacks fuelled in part by Muslim anger at stepped-up Jewish visits to a contested Jerusalem shrine, as well as by long-deadlocked peacemaking with Israel.
Eleven Israelis have been killed in stabbings, shootings, or other attacks. Israeli forces have shot dead at least 70 Palestinians, including 42 who Israel says were carrying out or about to carry out attacks. Many were teenagers.
Near the West Bank city of Hebron, the Palestinian woman tried to ram her car into a group of Israeli soldiers, a military spokeswoman said. The soldiers opened fire and wounded the woman, who was taken to an Israeli hospital. The hospital said she died before being admitted.
Medics from the Palestinian Red Crescent who initially attended at the scene said the woman was shot 15 times.
Soon after, near the Jewish settlement of Beit El, an Israeli civilian was stabbed by an assailant believed to be Palestinian. The attacker fled the scene and was being searched for, the Israeli military said.