"A launch [of a rocket] from the Gaza Strip aimed at hitting the Israeli territory has been registered", the statement said.
"We will defend Israeli civilians", it added.
The rocket attack on Beersheba was the first in months and the first that hit an Israeli home there since the 2014 summer war between Israel and Gaza's militant Hamas rulers.
The Magen David Adom medical service said a woman and her three children, whose home in Beersheba was struck, were being treated for shock after they fled to their shelter upon being awaken by warning sirens shortly before 4 a.m.
Another rocket from Gaza struck a beach near one of Israel's larger cities.
It was unclear who fired the projectiles but the Israeli army says it holds Hamas accountable for what is happening in the territory under its control.
The attack came as Defense Minister Avigdor Liberman called on the Israeli security cabinet to authorize a full-scale operational military campaign on the Gaza Strip, following months of ongoing violence and riots along the border.
The rioters carried burning tires, Molotov cocktails, hand grenades, rocks and live fireworks, all of which they threw at Israeli soldiers who were stationed on the other side of the border, to secure the region from terrorist infiltration.
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Meanwhile Turkish officials are widening their investigation after searching the consulate on Monday. The Journal , like CNN , said the Saudi statement has not been finalised.
Lieberman ordered the closure of the Kerem Shalom goods crossing and the Erez crossing for people, and the reduction of the permitted fishing zone along the Gaza coast to three nautical miles, the defense ministry body responsible for Palestinian civil affairs, COGAT, said.
A photograph of a Palestinian protester taking part in the Great March of Return in the occupied Gaza Strip won a top prize Saturday in France's prestigious Bayeux Calvados-Normandy Award for War Correspondents.
"If it has any sense, Hamas will cease its fire and violent outbursts - now", he said Sunday.
"Unfortunately neither the minister of defence nor the prime minister, nor the prime minister together with the minister of defence can make such a decision on their own", he said.
The rocket attack comes as an Egyptian delegation arrived in Gaza on Tuesday led by Ahmed Abdul Khaleq, an intelligence official in charge of the Palestinian file.
He also suspended shipments of fuel that had been trucked daily into Gaza over the previous week under a deal brokered by the UN and backed by the United States, Israel and others.
Seven were killed and hundreds injured during the most recent protests on Friday, with Lieberman later suspending fuel supplies to the already energy-starved Gaza Strip.
The UN says Israel's 11-year blockade of the enclave, ruled by Hamas, has resulted in a "catastrophic" humanitarian situation.