Hossein Karroubi, eldest son of Mehdi Karroubi, was detained by officials for publishing a letter his father sent last year to President Hassan Rouhani, according to Ebtekar daily and ILNA news agency.
"Karroubi wrote a letter in (April 2016) to the president and demanded... A trial from an authorised court to examine his charges," said Hossein's lawyer, Mohammad Jalilian.
Mehdi Karroubi has been under house arrest along with fellow opposition figure Mir Hossein Mousavi since 2011, following the violent protests that erupted against the re-election of former president Mahmoud Ahmadinejad in 2009.
Security officials have filed a complaint against Karroubi's son for "propaganda against the regime", the lawyer added.
Hossein Karroubi denies the charges and said he will appeal the decision.