The ministry said that women and children were among the dead, but did not give further details as to the identity of the victims.
An AFP journalist in Gaza saw the top of a building on fire after the strikes as well as ambulances evacuating victims.
The Israeli army said it had targeted three leaders of Islamic Jihad, which it considers a terrorist organisation.
The militant group confirmed three senior officials were killed, naming them in a statement as Jihad Ghannam, secretary of the Al-Quds Brigades military council, and Khalil al-Bahtini, also of the council and commander of the military wing in northern Gaza.
The third, Tareq Ezzedine, was described by Islamic Jihad as “one of the heads of military action” in the occupied West Bank who operated from Gaza.
In Rafah, in the south of the Gaza Strip, an AFP photographer saw the body of a man identified as Ghannam.
“We mourn the leaders and their wives and a number of their children who were killed in a cowardly Zionist crime,” Islamic Jihad said in a statement, vowing “the blood of martyrs will increase (the) resolve” of the movement.
The air strikes, which began a little after 2 am (2300 GMT), were still going nearly two hours later, according to AFP journalists, with a new explosion heard in the east.
The operation comes less than a week after Islamic Jihad announced a truce around Gaza – brokered with help from Egypt – following a fresh flare-up in violence.
Israel and Gaza militants traded cross-border fire following the death in Israeli detention of Khader Adnan, who had been on hunger strike for 87 days following his arrest over ties to Islamic Jihad.
On Tuesday, the militant group said Israel had “scorned all the initiatives of mediators” and vowed it would “avenge the leaders” killed in the latest air strikes.
– Roles of militants –
In separate statements detailing each of the Islamic Jihad figures killed, the Israeli army affirmed it would “continue to operate for the security of the civilians in the state of Israel”.
The military presented Ghannan as “one of the most senior members of the organisation” who “was entrusted with coordinating weapons and money transfers between the Hamas terrorist organisation” and his movement.
Bahtini was “responsible for the rocket fire toward Israel in the past month”, Israel said.
Ezzedine was recently “planning and direction (sic) multiple attacks against Israeli” civilians in the West Bank, where he was from and which has been occupied by Israel since the 1967 Six-Day War.
He was sentenced to 25 years in prison by Israel for his involvement in suicide attacks in the 2000s, before being freed in a 2011 prisoner exchange and transferred to Gaza, according to the army.
Israel and Gaza militants have fought multiple wars since Hamas took control of the Palestinian enclave in 2007.
A three-day conflict last August in Gaza caused 49 Palestinian fatalities and none on the Israeli side.
Tuesday’s casualties bring to 120 the number of Palestinians killed in the Israeli-Palestinian conflict so far this year.
Nineteen Israelis, one Ukrainian and one Italian have been killed over the same period, according to an AFP count based on official sources from the two sides.
