Margaret Hassan was taken by an unnamed group on her way to work in Baghdad, and a video of her has been shown on Arab TV channel al-Jazeera.
She has lived in Iraq for 30 years and is married to an Iraqi. Her husband Tahseen Ali Hassan has said he hasn't heard anything from the kidnappers.
Mrs Hassan was well-liked in Iraq, which makes the kidnapping confusing.
Mr Hassan said his wife hadn't received any threats before the kidnapping.
"This is a humanitarian organisation which has been serving the people of Iraq for 30 years," he added.
Care International was thought to have about 30 Iraqi staff working in its Baghdad office.
Its foreign staff were pulled out of the country in November.