Israeli officials were unavailable for comment immediately after the announcement of the judge's decision.
A Hamas leader in the Gaza Strip reportedly called the ruling "a criminal act."
Duffy ordered that Marzook be held in a New York federal prison until he is turned over to Israeli authorities. Marzook, 45, was arrested last July as he tried to enter the United States, where he had been living for several years.
Israel has requested the extradition, charging that Marzook engaged in a conspiracy to commit murder and other crimes against Israelis and has raised money for the military wing of Hamas.
"Marzook is responsible for atrocities and crimes perpetrated against our population and we would like to try him and sentence him for these crimes," Israel's ambassador to the United States, Itamar Rabinovich, said in March.
U.S. prosecutors also have charged that Marzook raised money for arms for Hamas and recruited terrorists.
Marzook has described himself as the head of the political bureau of Hamas and has denied he raised money in the United States to send abroad.
He also has denied that Hamas has any organized activity in the United States.
"Hamas' only structure is inside Palestine," he told The New York Times recently. "There is no organization outside."
Stanley Cohen, Abu Marzook's lawyer, said that he will appeal the ruling, a process that could take years.
"For those people waiting to strike up the band in Tel Aviv, tell them to put the tubas away," Cohen said. "This is just the first step."