"Today Mohammad Taghi Karroubi's passport was confiscated by security agents at Imam Khomeini International Airport," the website Sahamnews.org said.
"He was planning to fly to London for university related work, including the re-publication of his book 'Just or Unjust War?' and the completion of another book related to international law."
The second of three sons, Mohammad Taghi Karroubi is a professor whose book was previously published by "a well-known" British company, the website said, adding the authorities gave no explanation for the travel ban.
He had also helped to manage his father's unsuccessful campaign in last year's disputed presidential election.
Diplomatic ties between Iran and Britain have deteriorated since hardline President Mahmoud Ahmadinejad's re-election. Tehran has accused London of fomenting the post-election riots and detained nine British embassy staff who were later released.
The travel ban is the second blow to the politically active Karroubi family in less than a week.
On March 1, the Islamic republic's press watchdog revoked the licence of Irandokht (Daughter of Iran), a weekly run by Karroubi's wife Fatemeh and eldest son Hossein.
The watchdog said Irandokht was banned for "not meeting the conditions in the press law on practical commitment to the constitution."
Irandokht was first launched as a women's lifestyle magazine, but a new editorial team switched its coverage to political and cultural affairs two months ago.
Hossein said the decision to revoke Irandokht's licence was "the Ahmadinejad government's revenge on Mr (Mehdi) Karroubi for seeking the Iranian people's lost rights after the presidential election."
Last month, Karroubi's youngest son Ali was reportedly beaten and arrested by the security forces while trying to protect his father during marches marking the 31st anniversary of the Islamic revolution.
Karroubi has repeatedly accused authorities of abusing protesters detained during post-poll protests, including the rape of several male and female detainees.
Iranian officials have angrily rejected the rape allegations.
