Zenoorin on Thursday beat Nikita Glasnovic of Sweden 5-1 to collect the medal after winning a repechage match.
"I am so happy for Iranian girls because it is the first medal, and I hope at the next Olympics we will get a gold," said Alizadeh, who wears a head covering under her headguard.
Alizadeh thanked her parents and coach. "They really stand behind me and I am so happy," she added.
Fade Jones from Britain won the gold medal after she triumphed over Spain's Eva Calvo Gomez 16-7 in the same weight category.
Alizedeh won the 2014 Youth Olympics, and last year took the bronze medal at the world championships, beating Jones in her matches.
Few Iranian women have competed in the Olympics since the 1979 Islamic Revolution and have been hampered by stringent religious norms requiring specific clothing.
Women are not permitted to attend all-male athletic events or enter stadiums where they are taking place, a rule that has drawn international criticism on gender equality grounds.
