The 32-year-old, who is on a world tour, said authorities did not believe she would not "be playing a public show" in the country.
Wearing a white headscarf in a video posted on Instagram, she said: "We got detained and then we got deported."
And she wrote: "We were aware there couldn't be a public concert as I am a woman, and that is illegal in this country.
"Personally, I don't fancy going to an Iranian prison, nor am I trying to change the politics of the countries I visit, nor do I wish to put other people in danger.
"However, it seems the authorities don't believe we wouldn't be playing a public show so they have popped us on what they call the 'blacklist', as we found out when we turned up to the immigration hall."
The star, who rose to fame as a teenager, said: "After long discussions with the most friendly, charming and welcoming immigration people, the decision was made to detain us for the night and to deport us in the morning.
"Of course I was gutted. So close yet so far; this moment broke a little piece of my heart."
She told fans: "We were the ones that should have been apologising for not having our correct paperwork."
Stone posted images of herself boarding a flight to Iran's Kish Island in the Persian Gulf, which is an economic free zone that allows travel by all nationalities but can also be a dangerous place for Westerners.
Earlier this year, the singer crossed the border into Syria to perform in the war-torn country, later saying she was "just so glad nothing bad happened".