The defendant, who was 17 at the time of the attack, was tried as a minor, and convicted of rape and murder. The case was the first conviction in connection with the case.
The teenager was sentenced to three years in a reform home, the maximum penalty he could have faced. The time he spent in a juvenile home since he was arrested in December after the attack will count as part of his sentence.
Indian law forbids the publication of his name, though he has since turned 18. He had denied the charges, as do four adult men also on trial for the same attack.
The attack left the victim - a physiotherapy student - with such extensive internal injuries that she died two weeks later. The attack provoked national and international outrage and led to reforms of India's antiquated sexual violence laws. The government, facing immense public pressure - there were furious protests across India about the treatment of women in the country - promised swift justice in the case.
The defendants were accused of tricking the 23-year-old victim and her male companion into boarding an off-duty bus on December 16 after they had seen an afternoon showing of Life Of Pi at a shopping centre.
Police say the men raped the woman and used a metal bar to inflict internal injuries to her. They also beat her male companion. The victims were dumped naked on the roadside. The woman died from her injuries in a Singapore hospital, where she had been taken for specialist treatment.
Four of the other defendants are being tried in a special fast-track court in New Delhi and face the death penalty. The sixth accused man was found dead in his jail cell in March. The rest of the verdicts are expected next month.
The victim's family had called for the teenager to be tried as an adult, accusing him of being the most violent of the attackers.
Leaving the court in tears, Asha Devi, the victim's mother, said: "He should be hanged irrespective of whether he is a juvenile or not. He should be punished for what he did to my daughter."
A government panel set up to suggest reforms to sexual assault laws rejected calls to lower the age at which people can be tried as adults from 18 to 16.
On July 17, India's top court also refused to reduce the age of a juvenile from 18 to 16 years. However, it later agreed to hear a new petition seeking to take the "mental and intellectual maturity" of the defendant into account, not just age.
The victim's father said the family was deeply disappointed with the verdict.
"This is completely unacceptable to us," Badrinath Singh said. "We are not satisfied with this outcome. He is virtually being set free. This is very wrong."
SK Singh, a lawyer for the victim's family, said that they would challenge the juvenile court's verdict in a higher court.
"We will also seek a review of the man's age by a medical panel, since we believe he was not a juvenile when the incident took place," the lawyer said.
In India, especially in rural areas, many people do not have their births properly registered, and school certificates are used as proof of age.