Panahi was held at his home together with his wife Mahnaz Mohammadi, daughter and 15 guests on Monday evening, opposition leader Mirhossein Mousavi's website Kaleme said.
Panahi's home was searched and some of his belongings seized, it added.
The director supported Mousavi in last year's disputed presidential election, which plunged the Islamic Republic into months of political turmoil.
There was no immediate comment from the authorities and official Iranian media did not report Panahi's detention.
Last month, festival organizers said Iran had prevented him from traveling to the Berlin film festival. They said a travel ban had been imposed on Panahi, a winner of awards including the top prize at the Venice film festival for "The Circle" in 2000.
Iran's pro-reform opposition says the June poll was rigged to secure the re-election of hardline President Mahmoud Ahmadinejad.
The authorities denied the accusation of vote rigging and portrayed the huge opposition protests that erupted after the vote as a foreign-backed bid to undermine the clerical establishment.
Thousands of opposition supporters were detained after the election. Most of them have since been freed but more than 80 people have been jailed for up to 15 years. Two people put on trial after the election have been executed.
(Writing by Fredrik Dahl; editing by Michael Roddy)
