Two of the projectiles were intercepted by the Iron Dome aerial defence system, the army said.
The third struck a road, causing damage and a fire that was swiftly extinguished, according to Israeli media.
Sirens sounded in the city of Sderot, where a festival was taking place, and a number of other communities in the area.
The Magen David Adom emergency service said it treated seven people: six who was suffering from anxiety; and a 30-year-old woman who fell while running to the bomb shelter.
Overnight between Wednesday and Thursday, Israeli fighter jets struck a number of Hamas targets in Gaza in response to two rockets fired into Israel from the enclave.
A total of nine rockets have been fired from Gaza in just over a week.
No group in Gaza has claimed responsibility for the rockets. Spokesmen for the radical Islamist Hamas movement which rules Gaza have said the attacks were carried out by individuals and not by the group’s armed wing.
A Hamas spokesman warned last week that the difficult situation in Gaza would lead to a further escalation if Israel doesn’t show any commitment towards implementing understandings brokered by Egypt with Israel.
On Friday, Qatari envoy Mohammad Ammadi travelled to Gaza to hold talks with Hamas leaders on reinforcing ceasefire understandings with Israel, according to Palestinian security sources.
(Edited by Emmanuel Yashim)