Faezeh Hashemi recently met Fariba Kamalabadi, one of the leaders of the Baha'i community who had been allowed out of prison on a five-day break, according to Iranian media.
A photo of the meeting was published on social media in which Faezeh, wearing Islamic veil, is sitting next to Kamalabadi and other Baha'i women, all without the hijab.
Kamalabadi was arrested eight years ago with six other leaders of the Baha'i community and sentenced to 20 years in prison, for charges including espionage.
Outraged conservatives have denounced Hashemi's meeting and criticised the moderate former president Rafsanjani, along with some reformists in Iranian politics.
Rafsanjani himself has acknowledged his daughter had "made a mistake that needs to be corrected", according to local media.
"The Baha'i sect was created by the colonialists," he said. "This is a deviant sect... that we disavow and have always done."
But Faezeh said in an interview with Euronews Persian television that she had only visited "a friend".
Signup to our newsletter and follow us on Facebook and Twitter!
"It was a normal and harmless visit. I just visited a friend, that's all," she said.
Faezeh first met Kamalabadi when she herself was in jail in 2012 on charges of "propaganda against the regime".
But Grand Ayatollah Nasser Makarem Shirazi said Monday she should face prosecution, while merchants of the Grand Bazaar, a pillar of the regime, have launched a petition demanding the Tehran prosecutor take action, according to Iranian media.
The controversy comes as Washington on Saturday called on Tehran to release the seven leaders of the Baha'i minority faith.
John Kirby, spokesman for the State Department, also called on Tehran to "guarantee freedom of expression, religion, opinion and assembly for all citizens".
The Baha'i sect, founded in the 19th century in Iran, is not recognised by the authorities of the Islamic republic.
They are regarded as "heretics" and "spies" linked to Israel, because their centre is located in the northern Israeli city of Haifa.
Haifa on the Mediterranean seats the famous gardens of the Bahai World Centre, a pilgrimage site for the Bahai community.
In Iran, Bahai's do not have the right to higher education, to take up jobs in the government, or to hold group worshipping sessions.