"The jihadist mission came in response to the Zionist assaults against the Ibrahimi and al-Aqsa mosques and the continued Zionist aggression against our people in Jerusalem," Ansar al-Sunna said in a statement.
Al Jazeera's Jacky Rowland, reporting from the West Bank, said: "The Thai worker was hit by shrapnel and died.
"We have been aware for some time that groups loosely affliated to al-Qaeda have been operating out of Gaza and the fact that one of them is now publicly claiming responsibility for the attack is clearly a worrying message at a time when the EU foreign affair's chief [Catherine Ashton] is actually inside Gaza, visiting at the time of the attack," she said.
Ashton, who earlier visited a UN-run girls' school in the Jabalya refugee camp, said she condemned "any kind of violence".
"We need to move forward to get the peace process moving toward a successful resolution," she said.
The English baroness, who will later hold talks with UN officials, has made it clear she will not meet any officials from the Hamas movement which controls Gaza.
Since the beginning of 2010, at least 30 projectiles, including rockets and mortars, fired from Gaza have landed in Israeli territory.
But Thursday's death is the only one by a rocket in Israel since the end of last year's war in Gaza.
The name Ansar al-Sunna, which is also used by al-Qaeda allies in Iraq and elsewhere, brings to fore Salafist groups in the Palestinian enclave that have challenged Hamas' rule.