Iran’s Mizan news agency reported the execution, with the man accused of blocking a street and attacking a security force member with a machete in Tehran.
The Mizan news agency, run by the country’s judiciary, identified the executed man as Mohsen Shekari. He is believed to have been 23 years old.
Protests against Iran's government started last month when 22-year-old Mahsa Amini died in hospital after being arrested by Iran’s “morality police” and held in a re-education centre, allegedly on grounds her hijab was not being worn correctly.
The Iranian authorities have insisted she died of a heart attack. However, video footage circulated on social media has claimed she was beaten by officers during her arrest.
The morality police is allegedly now set to be disbanded, according to Iran’s attorney general, Mohammad Jafar Montazeri. Mr Montazeri said the force “had nothing to do” with the judiciary and would be shut down.
Iranian media said Mr Shekari had been convicted in Tehran’s Revolutionary Court, which typically holds closed-door cases that have been internationally criticised in other cases.
Reports said Mr Shekari had been arrested on September 25, then convicted on November 20 on the charge of “moharebeh” – a Farsi word meaning “waging war against God”.
That charge has been brought against others in the decades since the 1979 Islamic Revolution and carries the death penalty. It is believed more than 20 other people are facing charges which could result in a death sentence following the protests,
Amnesty International said: “The Iranian authorities must immediately quash all death sentences, refrain from seeking the imposition of the death penalty and drop all charges against those arrested in connection with their peaceful participation in protests.”
Mahmood Amiry-Moghaddam, director of the Oslo-based group Iran Human Rights, warned there could be “daily executions of protesters” if governments did not take action against Iran.
He tweeted Mr Shekari had been “sentenced to death in show trials without any due process” and said: “This execution must have rapid practical consequences internationally.”
Foreign secretary James Cleverly said: “[I’m] outraged by the tragic news of the first execution of a protester in Iran. The world cannot turn a blind eye to the abhorrent violence committed by the Iranian regime against its own people. The UK is opposed to the death penalty in all circumstances.”
Demonstrations have called for the resignation of Iran's Supreme Leader, Ayatollah Ali Khamenei, who has ruled the country since 1989. It is believed more than 300 people have been killed in the protests, including more than 40 children.
At the weekend, reports claimed the family home of Elnaz Rekabi, the Iranian climber who faced criticism from the Iranian government after competing without a headscarf, had been demolished.
Video footage showed Ms Rekabi's brother Davood – also an elite athlete – crying amid the rubble of the home. Sports medals can be seen on the ground. It is not known when the footage was taken.