Margaret Hassan, who has dual nationality and has been working for Care in Iraq for more than a decade, was seized by kidnappers at 7.30am (0430 GMT) on Tuesday, a spokeswoman said.
Aljazeera later aired footage of Hassan after her capture, sitting in a room and looking anxious.
The station showed close-ups of Hassan's identification cards and said the video was accompanied by a claim of responsibility from an unnamed Iraqi group.
Hassan's husband told Aljazeera from Baghdad that his wife had been driving to work when she was taken.
"When my wife was approaching her office, two cars surrounded her vehicle. The kidnappers attacked the driver and took control of her car, driving off with her to an unknown destination," Tahsin Ali Hassan said.
"We haven't heard anything about the group and no one has
contacted us," he said.
The Care spokeswoman was keen to stress that Hassan saw herself as part of the Iraqi community.
"She sees herself as an Iraqi. Iraq is her home. She has been living there for many years and would never consider coming back to Britain," the spokeswoman said.
Engineer Ken Bigley became the first British captive to be killed in Iraq when he was beheaded by his captors - believed to be followers of the Jordanian fugitive Abu Musab al-Zarqawi - earlier this month.
The video included close-ups of
her identification cards
Prime Minister Tony Blair, who was attacked by Bigley's brother Paul for not doing enough to save him, said his government would do everything possible to secure Hassan's release.
"This is someone who has lived in Iraq for 30 years, someone who is immensely respected, someone who is doing her level best to help the country," he said.
"It shows you the type of people we are up against, that they are prepared to kidnap somebody like this."
A statement from the charity said Hassan is employed by Care Australia as its Iraq country director.
"As of now we are unaware of the motive for the abduction. As far as we know, Margaret is unharmed," the statement said.
"She sees herself as an Iraqi. Iraq is her home. She has been living there for many years and would never consider coming back to Britain"
"We are doing whatever we can to secure her release."
A Foreign Office spokesman said British officials in Iraq were trying to establish what happened and were in touch with interim-Iraqi authorities.
Ireland said it would also do all it could to secure the release of Hassan who was born in Ireland.
Care is one of the few international non-governmental organisations (NGOs) to maintain a continuous presence in Iraq.
Most others pulled their remaining foreign staff out of the country after two female Italian aid workers were taken captive for three weeks in September.