Spokesman Ashraf al-Qudra told AFP the woman was shot in the head east of Gaza City.
Qudra named her as Amal al-Taramsi, 43, saying she was the third woman to die in months of clashes that have seen at least 241 Palestinians killed.
The Israeli army did not immediately respond to the specific incident but said around 13,000 Palestinians had taken part in violent "riots" in multiple sites along the border.
"The rioters have burned tyres and hurled blocks, explosive devices and grenades towards (Israeli) troops and at the Gaza Strip security fence," an army spokeswoman said.
Troops were responding "in accordance with standard operating procedures", she said.
The army later struck two positions belonging to Gaza's Islamist rulers Hamas, it said. A Hamas security source said there were no injuries.
An AFP journalist said several thousand protesters gathered east of Gaza City, with stronger clashes than in recent weeks.
Protesters tried to destroy a barbed wire fence near the border and Israeli forces responded with gunfire and teargas.
At least 25 other Palestinians received gunshot wounds, al-Qudra said in a statement.
At least once a week since March, Palestinians have taken part in often violent protests with backing from Hamas.
Most of the Palestinians killed were shot in weekly clashes, but others have been hit by tank fire or airstrikes.
In June, a female Palestinian medical volunteer was shot dead in border clashes.
Two Israeli soldiers have been killed over the same period, one by a Palestinian sniper and another during an aborted special forces operation inside Gaza.
Protests have calmed in recent months amid an informal truce between Israel and Hamas.
Under the unwritten agreement, Israel has allowed Qatar to provide money and fuel to Hamas's government in Gaza in exchange for relative calm.
An expected delivery of new funds by Qatar did not arrive this week, sparking speculation Israel was holding it up.
Also Friday, a Palestinian man "attempted to stab IDF troops" stationed near the hardline West Bank settlement of Kiryat Arba, adjacent to the southern city of Hebron, according to the Israeli army.
"The troops and a civilian who was at the scene fired towards the assailant," who was wounded by the gunshots, the army said in a statement.
Soldiers evacuated the alleged assailant for medical treatment, it said, adding that no the soldiers were wounded in the incident.