Nationwide protests erupted after the 22-year-old woman Mahsa Amini's death in September as other detainees also face possible death penalty for their involvement in the protests.
Iran has executed a protester who was convicted of injuring a security guard with a knife and closing off a street in the capital, Tehran.
The semi-official Tasnim news agency on Thursday identified the person who was executed as Mohsen Shekari but gave no more details.
Nationwide protests that erupted after the death of 22-year-old woman Mahsa Amini on September 16 represent one of the biggest challenges to Islamic Republic since it was established in 1979.
Authorities have been cracking down on the protests and on Monday, the Revolutionary Guard praised the judiciary for its tough stand and encouraged it to swiftly and decisively issue judgements for defendants accused of crimes against the security of the nation.
Judiciary spokesman Masoud Setayeshi announced on Tuesday that five people indicted in the killing of a Basij militia member, Rouhollah Ajamian, were sentenced to death in a verdict which they can appeal.
Amnesty International has said the Iranian authorities are seeking the death penalty for at least 21 people in what it called "sham trials designed to intimidate those participating in the popular uprising that has rocked Iran".
“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," it said.
Iran has blamed the unrest on its foreign foes including the United States.