Aljazeera reported that Micah Garen, a French journalist who carries a US passport, along with his translator were abducted by unknown men in the southern Iraqi city.
The journalist is said to be an archaeological reporter and manager of Four Corners Media.
As well as covering thefts of archaeological artefacts in Iraq the documentary organisation's website says it is working on "documenting the life and experiences of American soldiers on the front lines in Iraq".
The French embassy in Baghdad was not immediately available for comment and a US embassy official said he was not aware of the report.
Last week, a British journalist was captured then released in Basra.