Those injured were mostly hit by flying glass while in neighbouring buildings, and it was not known if anyone was in the ministry at the time.
Ambulances and rescue services raced to the scene early on Thursday as a fire blazed in the building.
Houses and cars in the area were badly damaged by the force of the blast and much of the foreign ministry building was destroyed, witnesses said.
“This is state terrorism against the Palestinian people,” Taher al-Nunu, a Palestinian foreign ministry spokesman, said of the attack.
An Israeli military spokeswoman in Tel Aviv confirmed the air raid and said the ministry was “led by Hamas” and used by the governing Islamist group to further its activities.
The Palestinian foreign minister is Mahmoud al-Zahar, a Hamas leader.
Meanwhile, a separate air strike, near Deir el-Balah in the central Gaza Strip, killed an Islamic Jihad fighter and wounded another, witnesses said.
Palestinians said they were about to fire a rocket at an Israeli tank when they were hit.
Israel killed at least 24 Palestinians in Gaza on Wednesday, including nine members of one family in an air raid that destroyed a house where the army said senior Hamas commanders were meeting.
Israel has launched a series of air raids and land incursions into Gaza following the capture of an Israeli soldier by Palestinian fighters on June 25.