The group said in a statement sent to Aljazeera on Friday that Fairuz Yamulky, who works for an American company, was released after her company pledged to pull out all its branches operating in Iraq and cease dealing with the US troops.
The group claimed that the company is involved in the construction of a number of military camps and Baghdad airport.
Yamulky, who is of Iraqi origin and a mother of two, was kidnapped on 5 September while traveling by car in northern Iraq.
Yamulky's captors demanded $2.5 million and the release of 50 Iraqi women from jail, Kamal Yamulky, the captive's father told the Canadian daily National Post.
The captors also required that Yamulky's employer, GSF Cement and Sand Co, build 150 new houses in Iraqi cities to replace those hit by US bombs.
Over the last six months more than 100 foreigners have been seized in Iraq. Most have been freed but around 30 have been killed by their captors.