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Dozens of rockets were fired from the Gaza Strip towards Israel on Saturday morning.
Air raid sirens rang out across the south of Israel and could be heard in the greater Tel Aviv area, tens of kilometres to the north.
A 70-year-old woman was critically injured when a rocket hit a building in southern Israel, according to Israel's Magen David Adom rescue agency
Elsewhere, a 20-year-old man was injured by rocket shrapnel, they added.
Footage from Reuters news agency shows Israeli firefighters fighting flames in the city of Ashkelon, as thick plumes of smoke rose from charred out vehicles.
The office of Israeli Prime Minister Benjamin Netanyahu said security chiefs are due to meet as a result of the rocket strikes.
No one has immediately claimed responsibility for the rocket fire.