Paramedics rushed the victim to the hospital, authorities said, but she died shortly after arriving.
The Israeli Embassy in the United Kingdom confirmed the victim was British. The University of Birmingham later identified her as Hannah Bladon, a student visiting Jerusalem on an exchange program.
The embassy said in a tweet: "Our thoughts are with those who were injured and the family of the British woman who was killed in the terror attack in Jerusalem today."
A suspect was arrested at the scene. Security officials identified him as Jameel Tamimi, a 57-year-old Palestinian man from the East Jerusalem neighborhood of Ras al-Amud.
Despite the Israeli Embassy's characterization of the incident as a "terror attack," the alleged perpetrator's motive is unknown.
Tamimi suffers from "personal, mental, or moral hardship," according to the Israel Security Agency.
According to the agency, Tamimi was convicted of sexually abusing his daughter in 2011 and attempted to commit suicide this year by swallowing a razor blade.
The attack comes during the Easter and Passover holidays when police are on heightened alert because of the increase in tourism.