The medical service said two other Beersheba residents were injured during the panic to seek cover. There were no reports of serious injuries in Israel.
"In response to the rockets fired from #Gaza at #Israel overnight, IDF fighter jets have started attacking terror targets in Gaza", the IDF wrote on its Twitter page.
In retaliation Israel struck 20 targets in Gaza, killing one Palestinian, according to the Hamas-run health ministry. Five other Palestinians were wounded in separate attacks.
The rocket hit a two-story house in Beersheba before dawn, the Israeli military said.
Another rocket from Gaza struck a beach near one of Israel's larger cities.
In addition to sporadic incidents, Israel and Hamas have fought three wars in the past 10 years.
The Islamists and allied militant group condemned the latest rocket fire as "irresponsible".
The rocket was the first to hit an Israeli home since the 2014 war between Israel and Gaza's Hamas rulers.
Usually, Israeli civilians are encouraged to return to their routine as quickly as possible, but on Wednesday, school was canceled in Beersheva and areas near the Gaza Strip. "Hamas would not do something like this while Egyptian intelligence officials are in the Gaza Strip and hours before the arrival of the head of Egypt's General Intelligence Force".
Defence Minister Avigdor Lieberman ordered the closure of both of Israel's border crossings with Gaza on Wednesday following the attacks. Lieberman announced Wednesday that all crossings into Gaza were being shut in response to the attack and the fishing zone around Gaza was being limited.
Israel's defence minister said on Tuesday that months of violent Palestinian protests on the Gaza border can not be allowed to go on, urging cabinet colleagues to back tougher measures. The blockade has restricted Hamas' ability to govern and made life extremely hard for Gaza's 2 million residents.
The protests intensified as Egyptian-mediated cease-fire efforts faltered.
Last week, some 14,000 Palestinians rushed the border fence, burning tires and throwing rocks, firebombs and grenades at soldiers stationed on the other side of the barrier.
Since March, 155 Palestinians participating or attending the protests were killed.
"The correct response is that a terrorist who enters Israel from Gaza can not return alive".
Lieberman said that deadly clashes on Friday, after Israel helped facilitate diesel shipments to the fuel-starved Gaza Strip, were a turning point.
Israel Prime Minister Benyamin Netanyahu told his ministers on Sunday that if Hamas doesn't come to its senses "they will be stopped in a different way".
But Hamas leader Ismail Haniyeh responded by saying that "diesel and salaries wouldn't stop the violence". But he said Israeli policy dictated an "immediate and forceful retaliation" against Hamas because the groups controls Gaza. Repeated attempts to reconcile Hamas and the West Bank-based administration of Palestinian President Mahmoud Abbas have failed, adding to the desperation fueling the demonstrations.