The incident occurred this afternoon when the prison van was passing through south Delhi's Hauz Khas area, said a police official.
The inmate has been identified as Manoj, said a senior official who did not disclose any further details.
In a similar incident reported in August 2015, two inmates were allegedly beaten to death by seven others, including an infamous outer Delhi-based gangster, in a fight that broke out inside the prison van heading from Rohini court to Tihar jail.