The report on the IRNA news agency says Faezeh Hashemi was arrested Sunday while trying to cause unrest by chanting anti-government slogans in one of the main streets of Tehran.
Iran's opposition had called for a rally Sunday to mark a week since the deaths of two people in Feb. 14 clashes between security forces and opposition protesters in Tehran.
Rafsanjani's youngest daughter was also briefly detained in the unrest that followed 2009's disputed presidential election.
Hard-liners have criticized the moderate Rafsanjani for supporting Iran's opposition leaders.
