They were killed in an airstrike in Jafarawi in central Gaza, the ministry said, while her husband was injured.
The strikes came after two rockets launched from the coastal enclave hit the town of Sderot, near Gaza's northern border, police and the army said.
In Gaza, one Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials said.
Eight others were also injured in the attacks, the ministry said in a statement.
While there were no immediate reports on injuries, the IDF did show pictures of damage to the vehicle.
Smoke plumes could be seen rising from Gaza City Wednesday evening.
A statement by Hamas' military force said it was responsible for the rockets.
Air raid sirens sounded nearly nonstop in southern Israel from sundown on Wednesday, warning residents to stay in shelters as more than 80 rockets were fired in their direction.
Rockets fired from Gaza into Israel as seen from Sderot.
An Israeli minister said his government has rejected an European Union plan to link the Gaza Strip with the West Bank, according to Israeli media on Wednesday.
According to the IDF, the rockets were launched from the Hamas-run enclave and two were intercepted by the Iron Dome missile defence system.
One Palestinian rocket hit a house, Israeli media said, showing footage of houses and cars pockmarked with shrapnel.
In response to the rocket fire, the Israeli Air Force bombed 12 Hamas targets in Gaza.
Hamas warned Israel - with which it has fought three wars since 2008 - it would pay for the attack.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
The strikes came after two fighters from the military wing of Hamas, which rules Gaza, were killed by Israeli fire on Tuesday.
A senior member of Hamas, the Palestinian Islamist group that controls Gaza, said talks mediated by the United Nations and Egypt on a deal to tamp down tensions were in "advanced stages". One Israeli soldier was killed by a Gaza sniper during this period.
Over the past four months, 158 Palestinians have been killed by Israeli fire, including at least 120 in the protests near the fence and others in Israeli air strikes and other incidents elsewhere in Gaza, according to the Gaza Health Ministry and a local rights group.
The Swedish vessel, named "Freedom for Gaza", was intercepted on August 4th and taken to Israel's port Ashdod its organizers said - the second such boat of the "Freedom Flotilla" prevented from reaching Gaza.