accused Ram Singh committed suicide on Monday around 5 am by hanging himself inside jail number 3 of Tihar Jail.
Sharma also raised questions about the functioning of Tihar Jail, saying it was "shocking" that the administration could not protect the undertrial.
"Suicide in a high security jail like Tihar is a matter of serious security lapse. The authorities must conduct a thorough probe to ascertain what led Ram Singh to take such extreme step," she added.
Echoing similar sentiments, Delhi Commission for Women Chairperson Barkha Shukla Singh said that this is a matter of surprise that he hanged himself inside the jail.
"The whole world, India and we were waiting that these people would be hanged. Now if the main accused hangs himself inside the custody in the Tihar Jail, where security is supposed to be really tight, then it is a very surprising thing. As far as I know, he was being kept in a separate barrack. So, I feel that it is a very surprising and raises questions on the police authorities," she added.
Meanwhile, the Union home ministry has sought a detailed report from Tihar Jail administration hours after Singh committed suicide in his cell.
"The home ministry has demanded a detailed report from the Delhi Police and the Tihar jail administration into the suicide of Ram Singh," said minister of state for home RPN Singh.
Singh, who was to be produced before court today for its daily hearing, was rushed to the jail hospital where he was declared brought dead.
His body was taken to Deen Dayal Upadhyay Hospital for post mortem. Forensic experts have visited the Jail premises to collect samples.
Tihar jail sources said Ram Singh, the prime accused in the December 16, 2012, Delhi gangrape-cum-murder case, hung himself using his clothes probably his own shirt. The incident came to fore when the guard spotted him this morning.
Singh was the driver of the bus in which the 23-year-old physiotherapist student was gang-raped by him and his five associates, including a minor, in south Delhi after brutally beating her and her male friend.
Ram Singh, along with the other four accused, was charged with murder, gang-rape, destruction of evidence, criminal conspiracy, dacoity, unnatural sex and common intent in the case. The sixth accused is a Juvenile and is in an observation home.
Ram Singh's death has posed serious questions on the security provided to the accused as all of them were under 'suicide watch after they had stopped talking and interacting amongst themselves.
The Tihar Central Jail complex has several jails, each identified by a number. While Pawan, 19, and Akshay, 29, are held in Jail No 4, Vinay, 20, and Mukesh, 26, are in Jail No 7.
Singh was arrested soon after the December 16 incident from near his home in RK Puram. The girl died of her injuries on December 29, 2012 in the multi-specialty Mount Elizabeth Hospital in Singapore.