“When the suspect continued approaching, the soldiers fired towards the suspect’s lower body,” the military said, adding that no weapon had been found on the woman and that the incident was being investigated.
The Palestinian Health Ministry said the woman, in her 40s, was pronounced dead in hospital.
Israeli forces have been on high alert following Arab and Palestinian attacks that have killed 14 people in Israel since late March.
More than 20 Palestinians, many of them armed militants, have been killed by Israeli forces since January, while Palestinians have reported a rise in violence by Israeli settlers in the West Bank.
In public remarks to his cabinet on Sunday, Israeli Prime Minister Naftali Bennett said there would be no restrictions on security forces in stopping what he has described as a “new wave of terrorism”.
Palestinian Prime Minister Mohammad Shtayyeh condemned the killing of the woman, saying he held Israel “fully responsible for the consequences of this heinous crime”.
Hussein al-Sheikh, a senior Palestinian official, said Israel’s expansion of settlements on occupied land Palestinians want for a state and visits by far-right Israelis to the Al-Aqsa mosque compound in Jerusalem have led to escalation.
Al-Aqsa, in a part of Jerusalem that Israel captured along with the West Bank in the 1967 war, has been a flashpoint of violence, often during the Muslim holy month of Ramadan, which began last week.
The complex is revered by Muslims as the Noble Sanctuary and by Jews as Temple Mount, the site of two Biblical Temples.
In recent days, Israeli forces have mounted security operations in the West Bank city of Jenin, a Palestinian militant stronghold, where deadly clashes with gunmen have ensued.
Israel condemned on Sunday serious damage which it said Palestinians had caused to Joseph’s Tomb, a sacred Jewish site in the West Bank. Pictures published by Israeli media showed the tomb partly smashed and torched.
“Attacking holy sites is attacking the heart of a people,” Israeli Foreign Minister Yair Lapid tweeted. “We will bring the perpetrators to justice and repair Joseph’s Tomb.”
There was no immediate comment from Palestinian President Mahmoud Abbas’s office.
(Reporting by Maayan Lubell in Jerusalem and Nidal al-Mughrabi in Gaza, Editing by Jeffrey Heller and Andrew Cawthorne)