Posting on Instagram, a disappointed Stone appears in a video wearing a white headscarf saying: “Well, we got to Iran, we got detained and then we got deported”.
She said she knew solo performances by women were illegal, but still wanted to see Iran.
She wrote on Instagram: “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 authority’s don’t believe we wouldn’t be playing a public show so they have popped us on what they call the ‘black list ‘ as we found out when we turned up to the immigration hall.
“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.”
On the authorities, she said: "These people are genuinely nice kind people that felt bad that they couldn't override the system."
Under Iranian law, women cannot perform solo concerts, though women do play in ensemble bands and orchestras.
It's unclear what Stone planned to otherwise do in Iran, though her Instagram post described her desire to show “the positives of our globe”.
Iranian newspapers reported Stone's Instagram comments on Thursday, though there was no immediate government comment on her claims.
Stone earlier 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.
However, Kish also can be a dangerous place for Westerners. Robert Levinson, a former FBI agent on an unauthorized mission for the CIA, disappeared on Kish Island in March 2007. He has yet to be found.
While Iran denies being involved in his disappearance, his family and the U.S. say Iran's government holds him.
Stone came to fame in 2003 as a small-town teenager with a big, soulful voice, showcased on her best-selling debut album "The Soul Sessions" and hit singles including "Fell In Love With A Boy." She also has taken acting roles and is a friend to England's Prince William and his wife, Kate.