Another security official said three staff members were inside the building at the time but they were unhurt.
The official said one protester was wounded when a consular guard opened fire and that the protesters retaliated by setting fire to two consular vehicles.
More than 20 demonstrators were arrested.
Protests have been held across the Middle East against the four-day-Israeli air attack on Gaza, which has killed at least 360 Palestinians and wounded more than 1,600.
Many Arabs have accused Cairo of giving the green light to Israel's assault after Hosni Mubarak, Egypt's president, hosted Tzipi Livni, Israel's foreign minister, for talks just two days before the launch of the onslaught.
In the absence of Israeli embassies in most Arab capitals, Egyptian diplomatic missions have been a particular focus of the demonstrations.
Demonstrators in Beirut, Lebanon - angry over Egypt's response to Israel's raids on Gaza - attacked the Egyptian embassy, throwing stones before police used tear gas to disperse them.
Protests have also been held outside the Egyptian embassy in Amman, the capital of Jordan.
Egypt has come under heavy criticism from Arab and Muslim countries over its refusal to re-open its border crossing with the Gaza Strip at Rafah over the past year, thereby aiding Israel's blockade of the territory.
Mubarak announced on Egyptian television on Tuesday that the Rafah crossing will not be fully re-opened until Mahmoud Abbas, the Palestinian president, regains authority in the territory.
"We will not deepen the division and that breach [among the Palestinians] by opening Rafah border crossing in the absence of the Palestinian Authority and the European Union monitors," he said, making reference to a 2005 agreement over the border.
Thousands have also rallied in Jakarta, the Indonesian capital, to voice their opposition to the Israeli assault on Gaza.
Demonstrators waved Palestinian and Indonesian flags while some carried banners with slogans such as "Move Israel outside Palestine land".
Indonesia is the world's most populous Muslim nation and many Indonesians have been staunch supporters of the Palestinian cause.
The protest coincided with a condemnation of the raids by Susilo Bambang Yudhoyono, Indonesia's president.
"I have sent a letter to the secretary-general of United Nations as well as to the UN security council condemning the Israeli military attacks and urging swift action to resolve the conflict," Yudhoyono said.
"The security council must formally meet and issue a resolution to force Israel to end all attacks, so that Israeli and Palestinian can continue the peace process."
Jakarta has no diplomatic relations with Israel.