"Two female terrorists armed with scissors stabbed a man next to the (Mahane Yehuda) market," police spokeswoman Luba Samri said.
"An officer who observed the event approached, fired accurately and neutralised the terrorists," she added.
One of the attackers was killed, while the other was seriously wounded, she said.
Two male victims, aged 27 and 80, were taken to hospital with light injuries, Israel's medical service said. There were no further details on their identities.
Mahane Yehuda is Jerusalem's best known market and is a popular tourist destination.
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Around half of the Palestinians killed have been alleged attackers.
The attacks were originally focussed in and around Jerusalem but had shifted to the occupied West Bank, particularly in and around the flashpoint city of Hebron.
The stabbings were the first attack in Jerusalem in nearly two weeks.