The 40-year-old discus thrower did not stretch out his hands to the Duchess of Cambridge after she put the silver medal round his neck, as he clasped his hands to his chest.
Under Iranian culture, a man is forbidden to make formal contact with a woman who is not his relative; had Zadeh been presented the medal by a man, he would have shaken his hand.
A spokesman for the Duchess said that she was aware that Zadeh would not shake hands with her.
"Many male athletes from Islamic countries do not shake hands in public with women they are not related for cultural and religious reasons," he is quoted as saying by The Sun.
Great Britain's Aled Davies won the event, while Wang Lezheng of China finished third and picked up bronze.