33-year-old Singh hanged himself with the help of his clothes from the grills of his cell in Jail No 3 at around 5 AM, jail officials said.
"There is already an inquiry which has been ordered by Tihar Jail on suicide of the main accused. We are enquiring into the matter," R P N Singh, Minister of State for Home Affairs, said.
"Singh was not alone in the cell. Other inmates were present and a guard was also posted. But nobody came to know about it. Around 5 AM, he was found hanging," a senior jail official said.
Singh, who was to be produced before court for its daily hearing, was rushed to the jail hospital where he was declared brought dead. His body will be taken to Deen Dayal Upadhyay Hospital for post mortem.
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Forensic experts have visited the Jail premises to collect samples.
Mamata Sharma, National Women's Commission Chairperson, raised questions about the functioning of Tihar Jail, saying it was "shocking" that the administration could not protect the undertrial and demanded an inquiry.
Former Tihar Director General Kiran Bedi said only an inquiry will tell under what special watch was he and what happened to that watch. "How did this man give this watch a slip? I think we need to wait for the inquiry," she said.
Singh was arrested a day after the December 16 incident from near his home in R K Puram. His brother Mukesh is also an accused in the case along with four others.
The girl was raped in the bus by him and his five associates, including a minor, in south Delhi after brutally beating her and also her male friend. The girl died in a Singapore hospital on December 29.
Singh was the driver of the bus in which the girl was raped. His brother was driving the bus when the girl was sexually assaulted allegedly by them.