The incident took place in Jail No 3 at around 5 am and Singh, the driver of the bus in which the girl was raped, was found hanging, jail sources said.
Singh was arrested soon after the December 16 incident from near his home in R K Puram.
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.