"A terrorist who ran with a knife at a guard who was escorting a family at the Damascus Gate plaza was neutralised by police," a statement said.
"The terrorist is dead."
It described the man as a "member of a minority" -- the police term for an Arab -- without saying if he was a Palestinian or an Israeli citizen.
A wave of mainly stabbing attacks by Palestinians has spread fear in Israel.
Three Israelis were killed in attacks in Jerusalem on Tuesday, making it the city's bloodiest day in the current wave of unrest.
The upsurge in violence that began on October 1 has led some to warn of the risk of a third Palestinian intifada, or uprising.