Israeli television broadcast images of damage to homes and cars in the town of Sderot. Reports said it wasn't clear if one of those hurt was wounded by a rocket or by debris from the rocket defense system.
Eight rockets were fired from Gaza and four fell into Sderot settlement.
In Gaza, one Hamas militant was killed in the air strikes, as was a Palestinian woman and her 18 month old child, Palestinian officials said.
"I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's multiple rockets fired toward communities in southern Israel", said U.N. Middle East envoy Nickolay Mladenov in an overnight statement.
A truce between Hamas and Israel will be officially unveiled by the end of August, according to Turkey's official news agency Anadolu, quoting a Hamas source.
Israel has not commented on the reported casualties in Gaza yet.
A video has been circulating on social media that captures the terror that Israelis endure when Hamas launches rockets at them.
The last four months have seen an upsurge in violence along the Gaza-Israel border. Israel temporarily suspended fuel shipments to Gaza in July for similar reasons.
Later, Palestinians fired about 70 rockets across the border, and Israeli aircraft struck at least a dozen militant targets.
On Tuesday, Israeli airstrikes killed two Hamas members in Gaza.
The demonstrations have been fueled in large part by pervasive despair caused by the blockade that has caused widespread economic hardship and left the coastal territory with crippling fuel shortages and just a few hours of electricity a day.
Armed Israeli drones and F-16 warplanes have pounded various areas across the besieged Gaza Strip, killing at least a Palestinian and injuring several others. One vehicle was hit, the IDF Spokesman's Unit said; IDF tanks responded by attacking a Hamas position in the region.
The agreement stipulates Gaza's Rafah border crossing to Egypt will be permanently opened and the Kerem Shalom crossing, the blockaded enclave's only intake point for commercial goods, will ease restrictions "dramatically", according to the report. He said by the end of the month, all fuel supplied by the United Nations will run out "and the problem is there is no sign of renewed funding from donors in the horizon".