The protesters, including 55 wheelchair-bound patients of a hospital rebuilt by Care International and more than 30 deaf children, attended a rally in front of Care's west Baghdad headquarters.
Many carried pictures of Hassan, the director of Care International Iraq who was abducted on her way to work last Tuesday, and waved banners calling for her to be freed.
"We demand the release of this woman who exerted painstaking efforts in reconstructing Ibn al-Qif Hospital for spinal diseases," said a 25-year-old patient who took part in the protest.
Some reports estimated the number of protesters to be 200, but a Care International source in Jordan said the figure was closer to 1,000.
A teacher at an Iraqi school for the deaf brought 30 pupils to the demonstration.
"They all love her" she said. "She helped them with hearing aids besides reconstructing the school."
Hassan has worked for the charity in Iraq since 1991 and has Iraqi citizenship.
Care has set up a special team of senior staff to help secure her release, but her captors have still not identified themselves.
Insurgent leaders in the Iraqi city of Falluja have reportedly said they are not holding her hostage, and condemned her kidnapping.