The 35-year-old man, who was armed, was only lightly wounded and managed to draw his gun after she stabbed him in the back, police spokeswoman Luba Samri said.
The woman was taken to hospital in serious condition, she added.
The stabbing happened in the alleyways of the Old City not far from the flashpoint Al-Aqsa mosque compound which has been the focus of three weeks of deadly violence in annexed east Jerusalem and the occupied West Bank, an AFP correspondent reported.
It came just days after two Israelis were killed in a knife and gun attack in the Old City that prompted a temporary ban on Palestinians other than residents, business owners and schoolchildren entering the district.
Saturday’s attack was followed by another stabbing the following day in west Jerusalem.
According to police, a 19-year-old Palestinian stabbed and wounded a 15-year-old passerby before being shot dead while fleeing, although his family have contested that account.