According to prison spokesman Sunil Gupta, Ram Singh, 33, hanged himself in a New Delhi cell after making a noose with a blanket or clothing. He was in a cell with three other inmates, Gupta said.
The authorities have ordered an autopsy and inquiry into the death.
Singh's family and lawyers said the death should be treated as murder.
"My son has not committed suicide," Singh's father, Mange Lal Singh, said. "He has been killed. I used to meet him at court and he told me he was sodomized and beaten by inmates."
Human rights organizations say that prisoners are systematically subjected to abuse at Tihar Jail, which is one of the biggest prisons in Asia, with some 10,000 inmates.
"This is a well-planned conspiracy," Singh's lawyer V. K. Anand said. "There was no mental stress. He was happy. There are no circumstances to suggest he could have taken such an extreme step."
Ram Singh was the driver of a bus in which a fatal gang-rape took place on December 16 last year. He was accused of being the main assailant of a student and her mail companion. The woman was raped repeatedly and died two weeks later of her injuries.
The incident triggered nationwide protests and an ongoing debate about violence against women in India.
Singh was facing charges of murder, gang rape, abduction, destruction of evidence and criminal conspiracy in a special court that began last month. He had been due to appear in court on Monday, March 11.
His brother Mukesh and three more men are also on trial and face the death penalty. A sixth suspect on trial in a separate court faces a maximum sentence of three years in jail.
They have all pleaded not guilty.
V. K. Anand said it was in the interest of the other accused that an inquiry into Singh's death come up with results swiftly.
Calls for death penalty
One young woman in Delhi said on Monday it was "wrong. It should not have happened. It would have been better if he had received his deserved punishment after confessing."
Large parts of the Indian public have called for the suspects to be handed down the death penalty.
The mother of the victim of the gang-rape told the AFP news agency that she was upset and "wanted justice" for her daughter.
Her brother said he was "not very thrilled with the news that he killed himself because I wanted him to be hanged … publicly. Him dying on his own terms seems unfair. But, oh well, one is down. Hopefully the rest will wait for their death sentence."