Another 19-year-old civilian was killed when Israeli tanks firing machineguns stormed a housing project in Beit Lahiya.
Hamas claimed responsibility for the attempted suicide bombing and identified the woman as Fatima al-Nejar, a mother-of-nine.
The Israeli army said soldiers spotted the woman approaching them with an explosive device and threw a stun grenade at her. The woman detonated the device, killing herself.
During the day, Israeli troops periodically fought gun battles with Palestinian fighters.
Israel said troops were operating in suburbs around Beit Lahiya, but denied forces were in densely-populated areas.
Two Israeli soldiers were also wounded by anti-tank missiles, the army said.
Residents said the incursion into Beit Lahiya was one of the biggest since Israel launched its offensive in late June after fighters, including Hamas members, abducted a soldier in a cross-border raid from Gaza.
The objective was then broadened to target rocket-launching squads, who have killed two Israelis in the past week. Fighters say the rockets are a response to army assaults.
Israel has killed nearly 380 Palestinians in Gaza, about half of them civilians, since it began the offensive, hospital officials and residents say. Three soldiers have been killed.