The attack occurred on June 23.
According to the spokesperson, those killed included administrative staff, young men doing their military service, inmates and their family members visiting them, reported IRNA news agency.
Neighbours living in the vicinity of the prison were also killed or injured, he said.
Jahangiri told the news agency that the Israeli attack also caused heavy material damage, emphasising that the strike marked a “full-scale crime.”
Iran and Israel were engaged in a 12-day conflict this month.
The ceasefire put an end to the conflict.
Several foreigner prisoners are reportedly imprisoned in the infamous Iranian jail.