They say the activists were detained for violating "the values" of the Islamic Republic of Iran and chanting nationalistic slogans.
Sunday's rally was held in Pasargadae, 630km (390 miles) south of Tehran.
Cyrus, who ruled in the 6th Century BC, reputedly established the first universal declaration of human rights.
Activists believe that 30 October marks the day Cyrus conquered Babylon in modern-day Iraq and declared all peoples equal in his Achaemenid Empire.
He is said to have freed slaves, including thousands of Jews.