Mr Rafsanjani led Iran between 1989 and 1997
The grandson of the former Iranian president, Akbar Hashemi Rafsanjani, has been arrested by Iranian authorities as he entered the country.
Hassan Lahouti was arrested as he arrived in Iran from London on Sunday.
Mr Lahouti is the son of opposition supporter Faezeh Hashemi, who was herself detained briefly after opposition protests erupted in June.
Mr Rafsanjani currently holds several powerful posts, but backed a reformist candidate in the presidential election.
Mr Lahouti, 23, flew to London 10 days after the protests began, the opposition Rahesabz.com website reported.
He was taken to Evin prison in Tehran on the orders of a judge, it added.
The opposition protests were sparked by claims that the election was rigged in favour of President Mahmoud Ahmadinejad, an allegation the government denies.
Mr Rafsanjani was Iran's president between 1989 and 1997.
He is currently the head of both the Assembly of Experts, which has the power to supervise and replace the Supreme Leader, and the arbitration body, the Expediency Council.
He is thought to be a "critical conservative", and is a fierce opponent of Mr Ahmadinejad, who defeated him in the 2005 presidential election.
Mr Rafsanjani backed the opposition candidate, Mir Hossein Mousavi, in the 2009 vote.
Mr Mousavi's Green Movement has developed into the biggest challenge to the government since the Islamic Revolution in 1979.
Thousands of people have been arrested and dozens killed.
Opposition supporters have faced increasing pressure from the authorities, with some hardliners labelling them as "mohareb" - enemies of God who can be sentenced to death under Iran's Sharia law.
At least nine have so far been sentenced to death and two people have reportedly been hanged.