Alidoosti, 38, was arrested on Saturday, official media said, after a string of social media posts supporting the protest movement including removing her headscarf and condemning the execution of protesters.
The crackdown was sparked by the death in custody of Mahsa Amini, 22, which 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 protests.
Alidoosti has considerable international renown due to her performances 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 acclaimed movie "Leila's Brothers" in which she starred.
"The brave actress of Iran got arrested," fellow actor Golshifteh Farahani wrote on Instagram.
Farahani began her career in Iran but now lives in exile after falling out with the authorities.
"Taraneh Alidoosti is one of Iran's most talented and acclaimed actors... I hope she's free to keep representing the strength of Iranian cinema soon," Cameron Bailey, head of the Toronto International Film Festival, said on Twitter.
Prominent British actor of Iranian origin Nazanin Boniadi also took to social media in support of Alidoosti, saying she had been arrested for "posting a photo of herself without compulsory hijab in solidarity with the protestors."
'Power of women's voices'
Iran last month arrested two 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.
Authorities also arrested the actors Soheila Golestani and Hamid Pourazari in November after they featured in a video where a group of film and theatre figures stood silently without headscarves. They have also been released.
The New York-based Center for Human Rights in Iran said "women are being arrested and jailed in Iran for refusing to wear forced hijabs, including prominent actress Taraneh Alidoosti. The power of women's voices terrify the Islamic Republic's rulers."
During the street protests, banners of supreme leader Ayatollah Ali Khamenei have been set alight, women have openly walked down streets without headscarves, and demonstrators have at times sought to challenge the security forces.
Alidoosti's most recent social media post was on December 8, the same day Mohsen Shekari, 23, became the first person executed by authorities over the protests.
"Your silence means the support of the oppression and the oppressor", read a post on her Instagram account.
On November 9, she posted an image of herself without a headscarf, holding a paper with the words "Woman, life, freedom", the main slogan of the protests.
She had vowed not to leave Iran and said she was prepared to "pay any price to stand up for my rights."
Images have also circulated on social media of Alidoosti shopping in Tehran without a headscarf.
The judiciary's Mizan Online news website said the actor was arrested "by order of the judicial authority" as she "did not provide documentation for some of her claims" about the protests.
Her Instagram account with more than eight million followers was no longer accessible on Sunday.
The Oslo-based monitor Iran Human Rights said Iran's security forces had killed at least 469 people in the protests, in an updated toll issued on Saturday.
Iran's top security body, the Supreme National Security Council, said on December 3 that more than 200 people had been killed in the street violence, including security personnel.
Iran's security forces have arrested at least 14,000 people, according to the United Nations.