According to the website Destination Iran, "In Iran, it’s not possible to use your Visa Card, Master Card, American Express, Diners Club, etc. Here you won’t be able to withdraw cash from ATM machines, swipe your cards to buy things, etc. They simply don’t function while you’re traveling inside Iran. Reason: sanctions!"
However, Destination Iran makes the Iran Travel Card, which "is a prepaid card into which you deposit some Iranian currency and carry it around with you to buy things, get cash from ATMs and banks, etc inside Iran."
In 2020, American Express was listed as a divested security on the Michigan State Retirement System list of divested securities for active business operations in Iran.