Pappu - a drug addict - was arrested on July 18 in connection with a theft case. He was lodged in Jail no 1 of the high security prison, jail authorities said.
He was sent to a drug de-addiction centre a day later and returned yesterday from the centre, they said.
"Today, at around 10 AM, he jumped onto a moving truck hired by a PWD contractor to bring construction material.
"The truck was going out of the jail after unloading the construction material. But he fell down and sustained fatal injuries," Tihar Jail spokesperson Sunil Gupta said.