An MDA spokesperson said two gunshot victims, a father, 47, and son, 23, were in serious condition with “gunshot wounds to their upper body”.
A police spokesman told Army Radio that Saturday’s incident was a “terrorist attack” and that the assailant was “neutralised and injured”.
The incident comes a day after a Palestinian attacker killed eight people near a synagogue on the outskirts of the city.
On Thursday, Israel carried out a raid in the Jenin refugee camp in the occupied West Bank. Ten Palestinians were killed, including an elderly woman, after dozens of Israeli soldiers attacked a house the army claimed housed suspected fighters, leading to several hours of intense confrontations.
It was one of the deadliest Israeli army raids in the occupied West Bank since the second intifada, or Palestinian uprising, of 2000 to 2005.
Police arrested 42 Palestinians following Friday’s attack.
In a separate statement, police announced the force had been placed on the “highest level” of alert following the attack.
Before Friday’s shooting, at least 30 Palestinians had been killed this year and the Palestinian Authority, which has limited governing powers in the West Bank, said it was suspending a security cooperation arrangement with Israel.