The fire was opened at the site of the "City of David" archaeological site.
The victims are a 22-year-old ambulance volunteer and his 45-year-old father.
Both are in serious but stable condition with upper body injuries, according to The Jerusalem Post.
A video taken from an Arab neighborhood of Jerusalem is circulating on social media.
Shooting and screams are heard in the clip.
According to the latest information from the security forces, a 13-year-old boy from East Jerusalem started the shooting.
He was injured, he is detained and is currently being treated.
The police classified what happened as a "suspected terrorist attack".
In the evening of January 27, the shooting took place near the synagogue in the Neve Yaakov district.
Seven people died, three were injured.
The 21-year-old attacker was killed in a shootout with the police.
After the shooting near the synagogue, 42 people were detained.
A few hours after the attack, the police surrounded the house of the suspect in the Arab neighborhood of East Jerusalem and, in particular, detained his parents.
It is believed that the attack could be a revenge of the Arab population of the region for the rocket strike, which was carried out by the Israeli army on the night of January 27 in the Gaza Strip in response to the shelling by the Palestinian Authority of Ashkelon and other settlements in the south of Israel.
The two sides exchanged rockets after a raid by Israel's army, border police and joint security service on a refugee camp in Jenin, on the West Bank.
The Israeli side claims that the target of the raid were members of the radical group "Islamic Jihad", who were planning terrorist attacks.
According to the Palestinian Authority, at least 2 civilians were among the 11 dead as a result of the shelling.