A large group of masked militants dragged Moussa Arafat from his Gaza home on Wednesday and killed him in the street.
The cousin of late leader Yasser Arafat had been fired as head of public security in April following a corruption crackdown. Arafat's son, Manhal, 29, was abducted.
A militant coalition, the Popular Resistance Committees (PRC), claimed responsibility for what it called the "liquidation" of Arafat. The PRC consists mainly of former members of the Fatah movement, who have accused Palestinian leaders of graft.
"We have executed the will of God and the rule of law because he killed people, ordered assaults on fighters and he had a big file of corruption," PRC spokesman Abu Abir said of Arafat.
In a statement, President Mahmoud Abbas said no effort would be spared to arrest Arafat's killers and free his son. "This assassination will not undermine our efforts to impose law and public order."
Arafat had many enemies. He had survived several previous assassination attempts, including a car bomb attack last year.
Many factions and armed groups all hope for a slice of power in Gaza, the first entire territory Palestinians will have had to rule without an Israeli presence.