The early morning attack, which caused damage but no injuries, stoked growing fears in Zionist regime that the mass protests which have swept the West Bank over the fate of detainees held in Zionist prisons, could spread to Gaza.
Just three weeks before a top-level visit by US president Barack Obama, his first since becoming president, the Zionist regime has been grappling with fears that the rising anger over the prisoners could spark a third intifada, or uprising.
Tuesday's rocket marked the first time fighters had fired across the border in more than three months following an Egyptian-brokered truce deal which ended eight days of deadly fighting in November.
It was also the first time Gaza had got involved in the widespread prisoner protests which have swept the West Bank in the past fortnight, which came to a head on Saturday with news that 30-year-old Arafat Jaradat had died in custody after being interrogated for throwing stones.
Jaradat was arrested on February 18 and questioned by the Zionist regime's Shin Bet internal security services on suspicion of involvement in stone-throwing in November.
Five days later, he died, with a Palestinian minister saying that preliminary autopsy results showed he had died "as a result of torture."
Fighters from the al-Aqsa Brigades, an armed offshoot of Palestinian president Mahmud Abbas's Fatah party, vowed revenge at his funeral, and on Tuesday they said the rocket fire was a first response.
"In a preliminary response to the killing of our hero the prisoner Arafat Jaradat, we claim responsibility for firing a Grad rocket on Ashkelon at 6:00 am (0400 GMT)," the Gaza branch said in a statement.
Immediately afterwards, the Zionist regime restricted access via Erez and shut down operations at the Kerem Shalom commercial crossing into southern Gaza, citing a "government directive."
Israeli NGO Gisha condemned the move as "collective punishment" saying the timing "raises serious concern that this is not a travel restriction necessitated by a concrete and weighty security imperative but rather a punitive act aimed at Gaza's civilian population."
Hamas spokesman Sami Abu Zuhri said there was "no confirmation the rocket came from the Palestinian side," and blamed the Zionist regime as "responsible for the murder of Arafat Jaradat and all the consequences."
Initial results from an Israeli-Palestinian autopsy conducted on Sunday showed bruises on Jaradat's body, muscle damage and broken ribs, Palestinian prisoner affairs minister Issa Qaraqaa said.
But on Monday, the Palestinians sent a letter to the UN Security Council detailing further injuries, including six broken bones in his neck, spine, arms and legs, as well as other injuries.
It said the autopsy showed Jaradat "was subjected to severe beatings, abuse and medical negligence during his captivity, possibly amounting to torture."
The Zionist regime initially claimed Jaradat appeared to have died of a heart attack, but confirmed the postmortem showed "fractures in the ribs".
Meanwhile, Palestinian police prevented demonstrators from reaching an area near Jalame checkpoint in the northern West Bank where several mass protests have erupted into violence in the past 10 days, an AFP correspondent said.
Earlier, Abbas had instructed security forces to "maintain the calm" following a demand from The Zionist regime at the weekend that he act to cool the situation.