The statement said: "A political security unit of four and a driver entered the office of lawyer Mohammad Raadoun, the president of Arab Organisation of Human Rights in Syria (AOHRS), and escorted him to the political security office in (the port city of) Latakia."
"We urge all honourable people for solidarity with us in a campaign for his release," the statement said.
Officials were not immediately available for comment.
Ammar Qurabi, the head of the group's media office, said he thought the arrest on Sunday was related to statements issued by the group about the arrest of returning Islamists, under a silent amnesty.
De facto amnesty
Syria told its embassies in March to facilitate the return of exiles, in what campaigners saw as a de facto amnesty for people who were forced to flee the country.
Rights activists say hundreds of Syrians living abroad for political reasons have taken advantage of the opportunity, but some have come back only to be put behind bars.
The group became active when President Bashar al-Assad introduced a measure of reform after assuming power in 2000, and freed hundreds of political prisoners.
The authorities later cracked down on activists, rights groups say.