The mayor says he ordered his car to stop when he spotted the attack near City Hall in Jerusalem downtown on February 22.
Footage shows Mayor Nir Barkat striding towards the suspect before bringing him down as one of his guards points a gun.
The 27-year-old victim was taken to hospital. Police arrested an 18-year-old Palestinian over the incident.
They say the suspect had entered Israel illegally before the attack.
At a news conference afterwards, Nir Barkat said he and his bodyguard jumped out of the car, “the guard aimed his gun [at the attacker]… and we grabbed the terrorist until police arrived.”
Mobile phone footage shows Nir Barkat leaning over the suspected attacker as he is being held on the ground by several men.
The exact motive for the stabbing is not clear, but it is the latest in a series of attacks by Palestinians on Israelis in recent months.
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