The medical service said two other Beersheba residents were injured during the panic to seek cover.
The military said another rocket from Gaza landed in the sea, just off the coast of one of the larger cities in central Israel. No injuries were reported.
Following the attacks, schools in Beersheba were closed and Israel’s military chief was cutting short his visit to the United States to come back and manage the crisis.
As a first response, Israeli military jets pounded Hamas targets across the Gaza Strip. The Gaza Health Ministry said a 25-year-old militant was killed inside one of the posts targeted. Three other people were wounded.
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.
Beersheba, which is some 50 kilometers (30 miles) from Gaza, is the biggest city in southern Israel, with a population of around 200,000.
Israel and Hamas have fought three wars over the past decade and fighting has flared up on several occasions recently, though neither side appears to be interested in another full-blown war. Egypt has been trying to mediate a long-term cease-fire to stave off another confrontation.
In a rare move, seemingly aimed at easing the tensions, the so-called “joint coordination room of resistance factions” that includes Hamas, the Islamic Jihad and other groups issued a statement distancing themselves from the rocket fire.
“We reject all irresponsible attempts that try to change the direction and sabotage the Egyptian efforts, including the overnight firing of the rocket,” they said. “At the same time, we emphasize we are ready to confront the Israeli aggression.”
The head of Egyptian military intelligence, Abbas Kamel, is scheduled to visit Gaza this week to renew high-level cease-fire talks.
The rocket attack came a day after Israeli Defense Minister Avigdor Lieberman said the time had come to deliver a “heavy blow” to Hamas after weeks of escalating violence along the border. 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.