Jill Carroll, 28, a freelance reporter for the Christian Science Monitor and other media outlets, was abducted 10 days ago in Baghdad.
The video, which has not been authenticated, is the first sighting of her since she was taken at gunpoint.
The Qatar-based network, which did not say from where it obtained the video, on its website said the abductors identified themselves as members of a previously unknown armed group calling itself the Brigades of Vengeance.
In the video Ms Carroll is shown in front of a white background and appearing to speak, however no sound is heard.
More than 40 foreigners are currently being held in Iraq or have been reported missing since a wave of hostage-taking erupted in the war-torn country in 2004, including several Westerners.
US forces hunting for the woman last week raided a mosque in the west of the capital after a tip that "activities related to the kidnapping were being carried out inside," triggering angry protests from Sunni Muslim clerics.
Ms Carroll is the 31st media worker to have been kidnapped in Iraq since the start of the war in 2003, according to watchdog group Reporters without Borders.
She has been reporting from the Middle East for three years.
Her family issued a statement calling for her release.
"Jill is a kind person whose love for Iraq and the Iraqi people are evident in her articles," said the statement.
"She has been welcomed into the homes of many Iraqis and shown every courtesy. From that experience, she understands the hardships and suffering that the Iraqi people face every day.
"Jill is a friend and sister to many Iraqis, and has been dedicated to bringing the truth of the Iraq war to the world," it said.
Mass grave found
Meanwhile, a mass grave containing the bodies of 22 people believed to have been killed during a failed Shi'ite uprising against Saddam Hussein in 1991 has been discovered near one of Iraq's holiest cities, Najaf, according to security officials.
"A search is ongoing to find other bodies," one source said.
The discovery comes as Iraq remains in uncertainty following the December election, with Sunni Arab leaders angry over a decision to annul less than one percent of the votes because of fraud, although they did not rule out taking part in the new government.
A Shi'ite member of the five-judge panel trying the deposed dictator and seven former cohorts over a massacre of Shiites in the 1980s will take over as chief judge when the trial resumes on January 24.
Said al-Hammashi will hold the post on a temporary basis following the resignation of Rizkar Mohammed Amin, a Kurd, as the presiding judge in the high-profile case, chief prosecutor Jaafar al-Mussawi said.