"The Jerusalem Brigades, the military wing of the Islamic Jihad movement, announces its responsibility for the heroic martyrdom operation that took place in the town of Umm al-Fahm," the group said in a statement.
The attack came after a six week lull in Palestinian suicide bombings.
In continuing low-level violence, a 10-year-old Palestinian child was gunned down by an Israeli tank in the West Bank town of Ramallah on Thursday.
The boy was shot in the chest after he went outside to buy cigarettes for his father, the child's mother said.
Premature blast
Wednesday's suicide attack was triggered prematurely, the Jerusalem Brigades statement said.
The bomber was said to have detonated his explosives when police stopped him on his way to a "Zionist target".
Islamic Jihad said the blast was a message to Israeli Prime Minister Ariel Sharon on the 20th anniversary of the Sabra and Shatila massacres that the Palestinian resistance is not over.
An Israeli inquiry found Mr Sharon responsible for the slaughter in the Beirut camps, which saw Israeli-backed Lebanese Christian militiamen kill hundreds of Palestinians.
"This operation is a natural response to enemy crimes against our defenceless people. It is not the first, and it will not be the last," the group said.
At a recent meeting of Palestinian factions, some groups called for attacks to be restricted to the occupied territories.
Peace plan
Although it was the first suicide attack in Israel in more than a month, the Israeli authorities in recent weeks have apprehended a number of suspected bombers trying to enter the Jewish state.
The attack came shortly after Mr Sharon demanded a total cessation of violence before any start to a fresh peace plan proposed by international leaders.
But Palestinians have responded cautiously to the outlining of a "road map to a Palestinian state", announced by senior officials from an international quartet - the United Nations, European Union, United States and Russia.
Quartet plan
Phase 1 (2003): Palestinian elections, security reform, Israel pull back, humanitarian initiatives, security agreement
Phase 2: Palestinian state created
Phase 3 (2004-2005): Israeli-Palestinian negotiations on permanent status solution
Palestinian leader Yasser Arafat said he saw Israeli troop withdrawals as the key beginning for reforms and moves towards peace.
Mr Sharon said the only hope for the latest peace plan put forward by the international community would be for the Palestinians to end all attacks and reform their security forces.
"For there to be progress, there must be an absolute end to terror and violence," he told a cabinet meeting.