The video was reportedly shared with Ms Alinejad as part of the White Wednesday campaign, an online movement started by the journalist that encourages women to wear white as a symbol of protest against the mandatory dress code.
According to unconfirmed updates on Twitter, the woman in the video was arrested by police and is being detained, with countless people now calling for her release.
Police in Iran's capital announced last week that women will no longer be arrested for failing to adhere to the strict Islamic dress code.
"Those who do not observe the Islamic dress code will no longer be taken to detention centres, nor will judicial cases be filed against them," said Tehran police chief General Hossein Rahimi
However, this does not mean that women are free to walk around without a headscarf.
The hijab is still compulsory but those caught wearing an "improper hijab" — wearing the scarf loosely or having parts of their hair showing — will instead be forced to take Islamic classes rather than being arrested.
It isn't just the hijab protesters are rallying against, with protests breaking out in Mashhad last week over economic problems.
The unrest quickly turned deadly as it spread across the country, with protesters condemning the regime as a whole in the biggest test for the authorities since mass demonstrations in 2009.
Iran's Revolutionary Guards chief Muhammad Ali Jafari yesterday announced an end to the protests, saying that those rebelling against the government had been brought under control.
"Today we can announce the end of the sedition," General Jafari said, quoted on the Guards' website.
"A large number of the troublemakers at the centre of the sedition, who received training from counter-revolutionaries ... have been arrested and there will be firm action against them."
He said those behind the protests had "intervened massively on social media" but that "once restrictions were started, the troubles reduced".
The White House declared it would seek sanctions against those involved in the crackdown, with President Donald Trump tweeting out a message of support for the protesters yesterday.
- Additional reporting from AP