Palestinian TV named the dead as three brothers of a local figure in Yasser Arafat's Fatah movement, Iyad Sharif, and described them as "righteous martyrs".
No official cause was given for the blast but correspondents say it appears to have been a bomb detonating prematurely and one of the dead is believed to have been a militant.
Israeli forces have made new raids across the territories, picking up at least 16 who were on a wanted list.
The explosion ripped through a room in the middle of the two-storey building in the camp near the town of Beit Lahia, ruining much of the building.
Palestinian TV named the dead men as Mahmud Sharif, Hani Sharif and Abd-al-Hamid Sharif, adding that the injured belonged to the same family.
One of the dead belonged to the radical militant group Islamic Jihad and another, like Iyad Sharif, to Fatah.
Local residents were quoted by the Associated Press as saying they believed the dead men may have been handling a bomb which went off accidentally.
'Bus bombers'
Earlier on Friday, Israeli forces made an incursion into the south of the Gaza Strip, demolishing alleged bomb-making workshops in the town of Rafah.
One gunman was killed and six other Palestinians injured in fighting in the town.
The Israeli army said its forces blew up six workshops used to manufacture rockets and mortars.
They struck the morning after a rocket was fired at an Israeli village about four kilometres (two miles) from the edge of the Gaza strip.
Troops also mounted arrest operations in the West Bank, briefly taking over the village of Tubas which an army spokesman described as a "centre of terrorist activity".
Sixteen Palestinians on the army's wanted list were detained in the village near Nablus, the spokesman told the French news agency AFP.
They were, the spokesman said, "part of an infrastructure of terror" responsible the bomb attack on a bus near Safad on 4 August which killed nine and wounded 50.
Palestinian security sources confirmed the arrest in Tubas, but said only three of the detainees were wanted men - one a member of Hamas, another of Islamic Jihad and the third of Al-Aqsa Martyrs Brigades.