The family member, who spoke on condition of anonymity for fear of reprisals, said Shujaa al-Khafaji had received threats from unknown people in recent days warning him not to publish posts about the protests.
Al-Khafaji, 29, runs a popular Facebook page called "Brothers Iraq" that focuses on human rights violations. On Tuesday the page, which has 2.1 million likes, posted a video that showed what it said were people setting a checkpoint on fire after the protesters had left. It blamed government supporters for the fire.
A statement posted on the Facebook page and a family member said "unknown armed" gunmen stormed al-Khafaji's Baghdad apartment at dawn Thursday and took al-Khafaji as well as all of the family's computers and cell phones. The family member said the gunmen were heavily armed and masked.
Prominent Shiite cleric Muqtada al-Sadr tweeted after the arrest that he is opposed to silencing people, adding that those behind it should be held accountable.