Police say Ram Singh hanged himself in Tihar jail, Delhi, although defence lawyers have questioned this.
Ram Singh was one of five men being held in the case. They all deny the charges.
The brutal attack on the student in December outraged India and triggered a debate about the treatment of women.
A sixth suspect is being tried by a juvenile court.
Ram Singh's lawyer, VK Anand, told the BBC he was informed about his client's death by police.
Authorities say Tihar is one of the most secure and modern prisons in India. It is equipped with CCTV cameras, mobile phone jamming devices, scanners and metal detectors. The sprawling campus hardly looks like a prison.
It is also India's most high-profile prison, where a number of prominent politicians and businessmen facing trial in corruption cases have been lodged.
Therefore it is baffling how a high-profile prisoner like Ram Singh, who is on trial, could have taken his own life in a modern maximum security prison like Tihar.
"This is shocking news. There were no circumstances to suggest that he would commit suicide. He was happy with the trial, it was going on smoothly," Mr Anand told the Times Now news channel.
Tihar jail spokesman Sunil Gupta told the BBC that an inquiry had been ordered into the incident. He said Ram Singh's body would be taken for a post mortem examination later on Monday.
Mr Singh's death comes as a huge embarrassment for the authorities who are already under enormous pressure over the case, the BBC's Sanjoy Majumder reports from Delhi.
The website of Indian news channel NDTV, quoting jail officials, said Ram Singh had hanged himself at around 05:00 local time on Monday (23:30 GMT Sunday).
Another defence lawyer in the case told the BBC that he had met Ram Singh on Friday during a court hearing and found him in a "happy state of mind".
Case Timeline
16 December 2012: Student gang-raped on Delhi bus
17 December: Bus driver Ram Singh and three others arrested
18 December: Uproar in parliament, street protests in Delhi and elsewhere
21-22 December: Two more arrests, including a minor
29 December: Victim dies in Singapore hospital
7 January 2013: Suspects charged in court with abduction, gang rape, murder
21 January: Trial of five accused begins in special fast-track court
2 February: Five accused plead not guilty
28 February: Sixth accused charged in juvenile court
11 March: Ram Singh found dead in Tihar jail
"He looked happy. He had his dinner last night. Why should he commit suicide?" Vivek Sharma said.
Ram Singh and the four other adult defendants - his brother Mukesh, Pawan Gupta, Vinay Sharma and Akshay Thakur - have been on trial in a fast-track court.
They face 13 charges, including murder, gang-rape, kidnapping and destruction of evidence. If found guilty they face the death sentence.
The maximum sentence the juvenile would face if convicted would be three years in a reform facility.
The 23-year-old rape victim, who was not named for legal reasons, was with a male friend when she was attacked on a bus and thrown from the vehicle.
She died in a Singapore hospital on 29 December from massive internal injuries.
Ram Singh was accused of being the driver of the bus.
Tihar prison, which authorities claim is the largest in Asia, is India's most high-security prison.
The 55-year-old jail houses more than 12,000 inmates although it has an official capacity of about 6,000.
The complex includes nine separate prison facilities.
Media reports quoting the chief of Tihar prison Vimla Mehra say there were 18 deaths in Tihar prison last year, of which two were cases of suicide.
