No one else was hurt, the Israeli rescue services were quoted as saying.
A second rocket struck the Ashkelon National Park on Monday, Haaretz said.
One woman had to be treated for shock after the attack, which caused damage to some homes in the area.
Agencies quoted the Islamic Jihad, a Palestinian group allied to Hamas, as saying that it fired rockets into Israel on Monday.
On Sunday, Palestinian fighters fired three Qassam rockets at the western Negev, one of which exploded next to a schoolbus carrying children, Haaretz said.
At least 21 rockets hit the western Negev over the weekend, the daily said.
The incidents come as the Egyptian chief of intelligence wraps up talks with Israel about a ceasefire with Hamas to end rocket attacks and Israeli reprisals.
Israel wants the truce deal to include freedom for Gilad Shalit, a captured Israeli soldier, and an end to alleged arms smuggling from Egypt into Gaza.
Fuel supply resumed
In other news on Monday, Kaanan Obeid, a senior Gaza energy official, said that Israel had resumed its supply of fuel for a Gaza power plant idled two days ago.
He said he expected the power plant to start operating again later in the day.
Obeid said the plant was shut down on Saturday because it ran out of fuel, normally supplied by Israel.