Dramatic footage shows a row erupt as the irate man approaches the woman, shouting: "Fix your hijab or I'll get you arrested!"
Crowds of onlookers are seen gathering as the pair swap heated words in the middle of the busy street.
In response to the cleric's words the woman shouts: "Garbage!" and rips off her hijab before storming off in anger.
The video, which was uploaded on the Facebook group My Stealthy Freedom, described the cleric's behaviour as "humiliating and arrogant".
The caption reads: "This is the wrong culture that has been telling women for forty years now.
"Those who want to conquer women always betray the concept of struggle and freedom."
Since the Iranian Revolution of 1979 the law has dictated that women have to cover their hair in public – and risk being jailed if they don't comply.
My Stealthy Freedom – which now has more than a million followers – encourages women to share photos of themselves without wearing the hijab in order to bring about a change to the law.
The group states: "If you are offended, film their ugly behavior.
"Let them publish their own responsibility for the ugliness of their behavior."
Journalist and campaigner Masih Alinejad, who founded the group, described the woman in the video as "brave".
She added: "This campaign is addressed to women who willingly wear the veil, but who remain opposed to the idea of imposing it on others."
Last month Iranian campaigner Shaparak Shajarizadeh was reported to have been sentenced to 20 years in prison after she was filmed standing on a traffic island in Iran's capital Tehran while waving her headscarf around on the end of a stick.
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