An Israeli military spokesman said troops had faced off with around 13,000 Palestinians, some of whom threw rocks and grenades across the fenced-off border. On three occasions, Palestinians crossed into Israel before doubling back, he said.
Gaza's health ministry, run by the Islamist militant group Hamas, says more than 220 Palestinians have been killed by Israeli troops in the protests, billed as pressing for an end to a grinding Israeli-led blockade of the enclave.
The 44-year-old woman killed on Friday was shot in the head, Gaza medics said.
Palestinians also want a right of return to lands from which their families fled or were forced to flee in the 1948 war of Israel's founding.
Israel says the protests are organised by Hamas to distract from its governance problems and provide cover for cross-border attacks. Hamas denies this.
On Friday, two senior Egyptian security officials left the territory after meeting with officials from Hamas and other factions. Participants said they discussed Cairo-led efforts to reconcile Hamas with the rival Palestinian president, Mahmoud Abbas, and reduce border tensions.