No one was injured in the rocket attack, but windows of an apartment block were shattered and parked cars in a residential area of the city were damaged, ending over a year of calm for the Israeli city closest to Gaza about 10km away.
Binyamin Netanyahu, the Israeli prime minister, said "Israel takes the firing on Ashkelon very seriously".
A police spokesman said the rocket fired was a 122mm, Chinese-made Grad, with a heavier payload and greater range than the crude, homemade rockets armed Palestinian group were launching almost daily until Israel's three-week military offensive into Gaza 18 months ago.
Zyara confirmed that the Israeli strikes "came after rockets were fired at Ashkelon", adding that "none of the Palestinian groups declared responsibility for that attack".
The Israeli military says it holds Hamas, which governs the coastal Palestinian territory, "solely responsible for terror emanating from the Gaza Strip".
Hamas says it is trying to stop armed groups from firing at Israel, but smaller groups have continued to launch rockets.
There were fewer injuries in the Gaza strikes than there could have been, given the crowded area that was hit, because Palestinians expected that "Israel would retaliate" for the attack on Ashkelon, Zyara said.
Push for talks
Israeli media said the Israeli government had lodged a protest with the United Nations for the Ashkelon attack.
In a statement, UN Special Co-ordinator Robert Serry said "indiscriminate rocket fire against civilians is completely unacceptable and constitutes a terrorist attack".
|No one was injured in the Ashkelon attack but windows were shattered [Reuters]
Hamas must not allow violence to undermine progress in talks between Israel and the Palestinians, he added.
Friday's violence coincided with diplomatic efforts to persuade Mahmoud Abbas, the Palestinian president, that he should advance from indirect negotiations to direct talks with Israel in pursuit of a Middle East peace pact – a course that Hamas and other armed groups in Gaza oppose.
Abbas, branded by Hamas as a pawn of the West, has been negotiating with Netanyahu indirectly for two months via a US mediator and is under pressure from Washington to upgrade to face to-face talks before the end of September.
On Thursday, Arab League foreign ministers meeting in Cairo gave Abbas the green light to engage in direct peace talks with Israel when he feels the time is right.
Hamas rejected the decision, calling it a "political sin".
Friday's rocket attack and military strikes also come amid a demand from the UN Human Rights Committee in Geneva that Israel lift its military blockade of Gaza – imposed since Hamas seized power there in June 2007 – and let an independent fact-finding mission investigate its raid on an aid flotilla on May 31 in which nine activists were killed by Israeli soldiers.
Israel has since eased restrictions on imports of food and consumer goods to Gaza but insists that the naval blockade must stay in place to help prevent shipment of weapons to hostile groups in the enclave.