Amanpour identified that no earlier presidents had requested this when she interviewed them exterior Iran.
She says a Raisi aide told her it was due to “the situation in Iran”.
The dying of a lady detained in Iran for allegedly breaking headscarf guidelines has sparked violent unrest there.
Mahsa Amini, 22, fell right into a coma last week, hours after morality police arrested her.
Officers reportedly beat Ms Amini’s head with a baton and banged her head against certainly one of their autos. The police have said there isn’t any proof of any mistreatment and that she suffered “sudden heart failure”.
The protests, now of their seventh day, have reached 80 other cities and cities within the Islamic Republic. At least 17 people have been killed.
The interview would have been Mr Raisi’s first on US soil, throughout his go to to the UN General Assembly.
Amanpour said she had been prepared to conduct it when one of many president’s aides insisted she lined her hair at Mr Raisi’s request.
“We are in New York, where there is no law or tradition regarding headscarves,” she said later on Twitter.
Amanpour said Mr Raisi’s aide had made it clear an interview wouldn’t happen if she didn’t put on a headscarf, saying it was “a matter of respect”.
Her workforce walked away from the interview refusing what she known as the “unprecedented and unexpected condition”.