There were no immediate reports of casualties in the air force strikes or from a rocket that landed in the city of Beersheba, 40 kilometres from the Gaza Strip.
One Islamic Jihad member was killed and 10 people wounded when an Israeli tank opened fire east of Gaza City on Wednesday.
Israeli television showed a crater in a street next to a badly damaged house in Beersheba.
Authorities have raised the alert level in southern Israel and braced for further attacks.
Israel said it held Gaza's Hamas rulers responsible for the violence, and Israeli Deputy Prime Minister Silvan Sahlom said Iran was trying to take advantage of unrest in the region.
"The rocket attack was a very grave act carried out by the agents of Iran, Hamas," he told public radio.
Also Wednesday a seven-year-old child was killed and two other people were wounded in an explosion apparently set off by accident and which also badly damaged a home in the southern Gaza city of Khan Younis, witnesses said.