The report also said the fight happened among prisoners jailed over drug-trafficking crimes.
It added that a number of the prisoners set blankets on fire in the open air.
The Iranian Judiciary’s news agency, Mizan, said now calm has returned to Karaj’s Central Prison and all inmates are in good health.
A Saudi-funded London-based TV channel earlier claimed that prisoners were shouting anti-government chants in the Karaj jail but the Judiciary’s news agency rejects this as basically-unfounded.