Celebrities and rights groups called on Iran on Sunday to free actor Taraneh Alidoosti, one of the most prominent figures yet arrested in its three-month crackdown on protests.

Alidoosti, 38, was arrested on Saturday, official media said, after making a string of social media posts supporting the protest movement including removing her headscarf and condemning the execution of protesters.

The unrest was sparked by the September 16 death in custody of Mahsa Amini, 22, whom the morality police accused of violating the Islamic republic's strict dress code for women.

Iran blames the United States and other "enemies" for trying to destabilise the country by fuelling the demonstrations.

Other Iranian actors and prominent figures including footballers have been detained in connection with the protests.

Alidoosti has considerable international renown, performing in award-winning films by director Asghar Farhadi, including the Oscar-winning 2016 film "The Salesman".

She attended this year's Cannes Film Festival to promote the movie "Leila's Brothers" in which she starred.

Fellow actor Golshifteh Farahani, calling her "the brave actress of Iran", noted her arrest in a post on Instagram with a photo of her and Alidoosti together and the Persian hashtag "free Taraneh Alidoosti".

Farahani now lives in exile after falling out with the authorities.

Cameron Bailey, head of the Toronto International Film Festival, called Alidoosti "one of Iran's most talented and acclaimed actors".

"I hope she's free to keep representing the strength of Iranian cinema soon", Bailey wrote on Twitter.

Nazanin Boniadi, a prominent British actor of Iranian origin, also backed Alidoosti on social media, saying she had been arrested for "posting a photo of herself without compulsory hijab in solidarity with the protestors."

Authorities in Tehran on Sunday also questioned pop singer Amir Maghare.

The judiciary's Mizan Online news website said the 26-year-old had "left the prosecutor's office after providing explanations, receiving a warning and making a commitment".

Daily sports newspaper Khabar Varzeshi reported Sunday that Ashkan Dejagah, 36, a former Iran national football player who also has German citizenship, has been barred from leaving the country "after being seen in protests... in Germany".

Dejagah, 36, joined Iranian club Foolad earlier this year after a career in Britain and Germany.

Iran last month arrested two other prominent actors, Hengameh Ghaziani and Katayoun Riahi, who expressed solidarity with the protest movement and removed their headscarves in public. Both have now been released on bail.

Ghaziani was among a group of actors who gathered outside Evin prison in support of Alidoosti, the reformist newspaper Shargh reported.

The group also included film star Mitra Hajjar, whose arrest Shargh had reported on December 3. (AFP)