The incident occurred in a train carriage on the light rail network near the walled Old City.
Video footage broadcast on television showed police officers restraining a man and carrying him away.
Israel's national ambulance service, Magen David Adom, said on Twitter they treated a 25-year-old woman who was in a critical condition after being stabbed in the upper part of her body. And so we will continue to do.
Ms Bladon, 20, a student at the University of Birmingham, had been on an exchange programme with the Rothberg International School at Hebrew University of Jerusalem since January.
The Foreign Office confirmed a Briton's death, saying it is supporting her family.
"This is one of many instances where a Palestinian suffering personal strife. chooses to carry out an attack in order to find release for his problems", the Shin Bet statement said.
Israeli authorities also revealed that the suspect "previously tried to commit suicide by attempting to swallow a razor blade".
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Police had been on high alert for Passover when tens of thousands of Jews pray at the Western Wall inside the Old City and some visit the flashpoint Al-Aqsa mosque compound above it.
The attack occurred as Christians marked Good Friday and Muslims held prayers at respective holy sites nearby.
The attack took place near the Old City that was packed with Christians, many of them tourists from around the world, celebrating the Good Friday holiday, as well as Jews celebrating Passover.
Apart from Friday's fatality, Palestinians have killed 42 Israelis and two visiting Americans since September 2015, mainly in stabbings, auto ramming assaults and shooting attacks. At least 242 Palestinians have died during the period of sporadic violence.
The family of Hannah Bladon, the British student stabbed and killed in Jerusalem, say they are "devastated" by the "senseless and tragic attack". Others died during clashes and protests.
Palestinian fears that Israel will seek to change those rules have been the source of repeated violence.
It was the latest bloodshed in a wave of attacks by Palestinians mostly acting on their own against Israeli civilians and security forces that erupted in 2015.
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