Eitas Youssef, 41, was reportedly killed and her two daughters, aged 22 and 20, were slightly injured when the troops opened fire as they surrounded a house in the town of Tulkarem to arrest an alleged militant
The soldiers had converged on the house in around 20 jeeps, the Palestinian source said.
An Israeli army spokesman told AFP that "shooting broke out when a top official of (radical Islamic movement) Islamic Jihad in Tulkarem resisted arrest."
"The soldiers opened fire after having noticed suspicious movements around the house. Before that they had been calling on the Palestinian militant to hand himself over for one and a half hours and fired warning shots in the air," the spokesman said.
Several people were reportedly arrested during the Israeli military operation in the West Bank.
Monday's death brings the overall toll to 5,035 since the Palestinian uprising began in September 2000, the vast majority of them Palestinians, according to an AFP count.