The woman, who was attacked by five men on a public bus in 2012, later died from her injuries. The attack provoked outrage around the world.
A spokesman for the New Delhi police told CNN the interview was banned because of its potential to breed disorder.
"A police case has been registered, and we have obtained restrain(ing) orders from the magistrate against the interview," Rajan Bhagat said Tuesday. "No channel beaming into India, local or foreign, can air it. It cannot be published either."
Mukesh Singh, a bus driver, was one of the five men convicted in the gang rape case and sentenced to death by hanging. He and three others are appealing the sentence. Singh showed no remorse, for what he dubbed "an accident" that occurred on December 2012 to a BBC Storyville documentary crew.
"A decent girl won't roam around at 9 o'clock at night," he told the BBC. "A girl is far more responsible for rape than a boy. Boy and girl are not equal.
"Housework and housekeeping is for girls, not roaming in discos and bars at night doing wrong things, wearing wrong clothes."
He suggested that they "had a right to teach them a lesson."
The father of the girl, known as Nirbhaya, told CNN he had read Singh's comments.
"He has challenged society and the judicial system. The death sentences handed down in this case should be carried out without delay and the appeals dismissed," said Badrinath Singh.
Meanwhile, a defense lawyer in the case distanced himself from Singh's comments, calling them hurtful.
"He shouldn't have given this interview," said defense attorney A.P. Singh. "There was no need for him to speak like that from the jail. His comments have further hurt public sentiments," Singh said.
A senior Indian supreme court lawyer not related to the 2012 rape trial said the convict's remarks would further strengthen the prosecution's demands for dismissal of his appeal. "He showed no remorse or repentance," said advocate Dharitry Phookan. "Personally, I think the man just made the case of death sentence against him much stronger," she added.
Bus driver's comments
On December 16, 2012, the 23-year-old female victim had gone to watch "The Life of Pi" with a male friend at a New Delhi mall and boarded the bus.
Mukesh Singh was the driver, and the men on the bus dragged the woman to the back and took turns raping the woman, using an iron rod to violate her as the bus drove around the city for almost an hour. They also beat her male friend.
When they had finished, they dumped the two victims by the side of the road.
The brutality of the attack galvanized the nation, triggering mass demonstrations and cast a spotlight on the treatment of women in India.
Singh seemed puzzled about why the gang rape became such a touchstone issue, wrote Leslee Udwin, director of the documentary.
The woman's injuries were so severe that some internal organs had to be removed. She died two weeks later at a Singapore hospital.
She suffered injuries to her abdomen, genitals and intestines, which Udwin read aloud to Singh
at one point during the 16 hours of interviews.
He remained defiant and showed no remorse, Udwin wrote.
"When being raped, she shouldn't fight back," Singh told the BBC, saying she should've permitted the assault. "Then they'd have dropped her off after 'doing her.' "
'Her life was of no value'
Singh said the death sentence as a punishment for rape will only endanger more women.
"Now when they rape, they won't leave the girl like we did. They will kill her. Before, they would rape and say, 'Leave her, she won't tell anyone.' Now when they rape, especially the criminal types, they will just kill the girl," Singh said.
Jail authorities told CNN that Singh's interview was conducted in 2013, but it's unclear whether it was filmed before or after the convictions. Under Indian law, no media interview in custody is admissible in law. But it remains unclear how Singh's comments may affect his appeals process.
Singh's brother, Ram Singh, was one of the six men charged with rape and murder, but he was found hanged in his jail cell in Delhi before the trial ended in March 2013.
Singh's lawyer echoed similar sentiments about women: "If my daughter or sister engaged in premarital activities and disgraced herself ... I would most certainly take this sort of sister or daughter to my farmhouse, and in front of my entire family, I would put petrol on her and set her alight."
The documentary filmmakers also interviewed other convicted rapists, one called Guarav, who admitted he had raped a 5-year-old girl and retold his story with a half-smile.
When she asked how he could commit such an act given how small and terrified she was, he gave her a look as if she was "crazy for even asking the question."
He replied, "She was beggar girl. Her life was of no value."
Despite the challenges facing women in India, Udwin acknowledges the efforts and the masses of both men and women who are demanding change in India's gender dynamics and equality for women.
"Their courage and determination to be heard was extraordinarily inspiring," she writes.
According to a BBC spokesperson, the documentary "provides a revealing insight into a horrific crime that sent shock waves around the world and led to protests across India demanding changes in attitudes towards women.
"The film handles the issue responsibly and we are confident the programme fully complies with our editorial guidelines."
It will release on International Women's Day on Sunday.