The Iran Human Rights Documentation Center said Hashem Shaabani and another man were hanged in prison Jan. 27, al-Jazeera reported Monday.
Shaabani, 32, had been in prison since early 2011.
In 2012, he appeared on state-owned television where human rights groups said he was forced to confess to "separatist terrorism."
Shaabani, who was called an "enemy of God," and 13 other people were found guilty in July of "waging war on God" and spreading "corruption on Earth."
Officials reportedly informed the men's families of their execution and that they would be notified of their burial places.
Shaabani, a critic of the government's treatment of ethnic Arabs in Khuzestan province, was the founder of Dialogue Institute and popular for his Arabic and Persian poems, al-Jazeera said.
More than 300 people have been executed since Hassan Rouhani became president in August, the IHRDC said.