Vinay Sharma is one of 4 men sentenced to death or gang-rape, torture and killing of Nirbhaya in 2012.
He tried to commit suicide on Wednesday night. He first took excessive painkillers and thereafter tried to hang himself with a towel in Tihar jail.
He has been admitted to the Deen Dayal Upadhyay Hospital in Delhi where his condition is critical.
Six men were found guilty of raping and torturing the 23-year-old physiotherapist, who was on her way home after watching a movie on a winter evening. She died in hospital 13 days later. As street protests raged through a shocked nation, the government introduced major changes to laws on crimes against women.
Vinay Sharma and three others have appealed against their death sentence in the Supreme Court.
The youngest of the rapists, who was short of 18 when he was arrested, was released from a correction home last year after three years in probation, amid protests by hundreds including the woman’s parents.