The Palestinian health ministry said the woman had died of her injuries. There was no word of Israeli casualties.
The incident follows a rise in tensions after a Jewish nationalist march in Jerusalem on Tuesday drew the launch of incendiary balloons across the Gaza border and retaliatory Israeli air strikes.
The Israeli military said the Palestinian woman "attempted to ram into a number of IDF (Israel Defence Forces) soldiers" near the Palestinian village of Hizma, northeast of Jerusalem.
"After the car-ramming attempt, the assailant exited her vehicle with a knife drawn ... The soldiers responded with fire towards the assailant and neutralised her," the military said in a statement.
There has been a rise in violent incidents in the West Bank in recent weeks.
Last Thursday, Israeli special forces killed an Islamic Jihad militant and two Palestinian security men in an exchange of fire in the northern West Bank city of Jenin.
Two Palestinians were killed in separate incidents on Friday and Saturday, the first during a clash with Israeli troops in the West Bank and the second while wielding a knife at military checkpoint near Jerusalem.
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