Rabbis Mendel Epstein and Martin Wolmark asked for more than $50,000 to hire "tough guys" to attack a recalcitrant husband with cattle prods, authorities said.
The men and eight other suspects appeared in federal court on Thursday.
Under Orthodox Jewish belief, a husband must grant permission for a divorce.
The permission comes in the form of a document known as a get.
In some Orthodox communities a woman who has not obtained a get may not marry again even if a civil divorce is finalised.
She may sue in rabbinical court, but some men ignore an unfavourable ruling, even if it means being estranged from the religious community.
The FBI investigation took place in Ocean and Middlesex counties in New Jersey and Rockland County in New York, and involved raids in both states, according to agency officials.
Two undercover FBI agents posing as a woman seeking a divorce and her brother called Rabbi Wolmark for help, and he connected them to Rabbi Epstein, according to a criminal complaint filed in federal court in New Jersey.
The undercover agents videotaped their meeting.
"Basically, what we are going to be doing is kidnapping a guy for a couple of hours and beating him up and torturing him and then getting him to give the get," Rabbi Epstein is quoted as saying during the conversation, according to the complaint.
He added that the "tough guys" would use electric cattle prods and handcuffs and place a plastic bag over the man's head, according to the complaint.
'For the money'
Rabbi Epstein also allegedly told the undercover agents that such instruments were unlikely to leave a mark, avoiding attention from authorities.
"Basically the reaction of the police is, if the guy does not have a mark on him then, uh, is there some Jewish crazy affair here, they don't want to get involved," he said, according to the criminal complaint.
The FBI said the price was more than $50,000, including $10,000 for a rabbinical court to approve the action. They had wired $20,000 to the accused before the arrests.
"They did it for money," Assistant US Attorney Joseph Gribko said during a hearing on Thursday.
"They didn't do it out of religious conviction."
Rabbi Wolmark's lawyer, Marc Agnifilo, argued his client was caught up in a case where religious law involving "an old tradition" collided with federal statutes.
No pleas were entered for the suspects, and all ten have been ordered held in federal custody until a hearing currently scheduled for next week.