Nine others were injured in the blast, the health ministry said.
Various social media accounts that belong to ISIS supporters have been sharing a statement they say is from the terror group claiming responsibility for the attack.
Egypt has seen escalating attacks by Islamist militants. The Saturday incident was the first attack targeting a consulate or an embassy in recent years.
No consulate staff were among the victims, Italy's Foreign Affairs Minister Paolo Gentiloni said in a tweet.
"Italy is not intimidated," he added.
The consulate is located in the heart of the city on a busy intersection. The Italian Embassy is in a different neighborhood.
The timing of the blast -- early in the morning on a weekend -- helped minimize casualties. On week days, the area is teeming with pedestrians and vehicle traffic.
"There's significant damage to the side of the building, a wall has collapsed and there was blood on the debris," photographer David Degner told CNN from the scene.
The explosion damaged the side of the consulate facing a vacant lot.
Degner said he saw at least one burned and twisted wheel.
Police pushed back a crowd of several hundred people who converged on the blast site, Degner said.
Militants have killed hundreds of policemen and soldiers since the overthrow of Islamist President Mohamed Morsy in July 2013.
Early last week, the chief prosecutor was killed in a car bomb targeting his convoy. Two days later, ISIS-aligned Ansar Beit Al Maqdis (now called the "State of Sinai") militants attacked 15 army outposts in North Sinai, killing 21 soldiers. Following an hours-long battle, the army said it killed more than 200 terrorists.
The government is discussing a new terrorism law that was criticized by local rights groups and the Journalists' Syndicate as counterproductive and unconstitutional.
Previously, militants mostly targeted Egyptian government officials and security forces.
But four people were killed and 14 wounded when Ansar Beit Al Maqdis targeted a bus of South Korean tourists traveling from Egypt's Sinai Peninsula into Israel in February 2014.
That month, it warned all foreigners to leave the country.
Egypt's army has struggled to crush the militants but the attacks go on.
In June, two assailants were killed and one injured in a thwarted attack
at Karnak Temple in Luxor, a popular destination for tourists.
The Egyptian government has been trying to lure back tourists for the summer high season.
Tourism represents 11.3% of Egypt's gross domestic product and 19.3% of its foreign currency revenues, Egypt's State Information Services says.