The Iranian lost to Japanese Kotaro Kiyooka 10-3 in the final match of the 65kg.
Amouzad defeated American wrestler Zain Retherford 8-0 in his first match and then beat Albanian representative Islam Dudaev 11-0 in quarterfinals.
Amouzad also defeated Hungarian Ismail Musukaev 10-0 in the semifinal.
Iran’s Hassan Yazdani in 86kg and Amirhossein Zare in 125kg have previously claimed two silver medals in the 2024 Olympics.