Rafsanjani's grandson, Hassan Lahouti, was arrested and sent to the Evin prison following his return from London, the BBC reports.
He is the son of opposition leader Faezeh Hashemi, who was arrested briefly following the unrest that greeted contested presidential elections in Iran in June.
Lahouti left for London shortly after violent June demonstrations began.
Rafsanjani, an influential cleric in the Iranian government, came under fire from the conservative leadership for backing opposition leader and former Prime Minister Mir Hossein Mousavi during the June contest.
Officials in Tehran blamed the former president for fanning the "fires of dissent" for his support of the opposition movement in Iran.
Government-backed security forces responded to civil demonstrations that followed a fiery August sermon from Rafsanjani with tear gas and mass arrests.
The former president also boycotted the inauguration of President Mahmoud Ahmadinejad in protest of his disputed victory in June elections.
2014: The Year in Music [PHOTOS]