The children, one of them just four months old, were injured when a powerful bomb destroyed the third and fourth floors of the ministry.
Doctors said the injured children were being treated at Gaza City's Al Shifa Hospital. They lived in nearby homes which were badly damaged in the powerful blast.
The latest strike comes a day after similar Israeli sorties killed 23 Palestinians, including seven children from the same family, making it the deadliest day since the assault began two weeks ago.
A total of 75 Palestinians have been killed since Israel launched a massive air and ground offensive on impoverished Gaza in a bid to release a teenage soldier captured by militants last month and end rocket attacks.
The Israeli offensive is aimed at securing the release a teenage soldier, Corporal Gilad Shailt, captured by militants last month and to end rocket attacks.
Abbas lashes out
Palestinian president Mahmud Abbas called killings "total aggression" and urged the US and Middle East quartet to intervene immediately.
The armed wing of the governing Palestinian movement, which claimed joint responsibility for the capture of Corporal Shalit on June 25, vowed a "strong and painful" response.
Just hours later, the Israeli army opened a new front in the Middle East crisis, launching a ground and air assault on Lebanon.
It followed captured two soldiers on Israel's northern border by Hezbollah guerillas.
In the West Bank city of Ramallah, Mr Abbas issued a statement "strongly condemning the Israeli crimes against Palestinian families, children and women in Gaza today".
He condemned what he said was an Israeli "escalation" saying that Israel was “complicating matters.”
Mr Abbas called for diplomatic efforts to be given a chance to end the crisis and called on the four Middle East peace sponsors, particularly Washington, to intervene.
Hamas leader targetted
Israel said Mohammed Deif, the leader of Hamas's armed wing, the Ezzedine al-Qassam Brigades was wounded.
Deif is believed to be the mastermind behind a wave of suicide bombings in the 1990s that killed dozens of Israelis.
A Palestinian medical source confirmed that Deif had been operated on but his life was not in danger. Another three Hamas military leaders were being treated at the hospital.
But Abu Obeida, a spokesman for the Qassem Brigades, categorically denied Deif had been hurt and slammed the "deceitful information intended to cover up Zionist crimes".
Israel has flatly refused to negotiate with Hamas or free Palestinian prisoners in exchange for Corporal Shalit, vowing the assault will continue "in places, in time, in measures" at its convenience.
Aid groups have expressed concern about the difficulties of providing assistance to 1.4 million people living in Gaza following months of financial crisis and the suspension of direct Western aid to the Hamas-led government.