The deadly blaze came amid nationwide anti-government protests, sparked by the death of 22-year-old Jina Mahsa Amini in police custody.
Iranian authorities have sought to distance the prison incident from the continuing protests over Amini's death.
Amini was arrested by Iran's morality police for violating the Islamic Republic's strict dress code. She died on September 16, three days after she fell into a coma following her arrest.