The woman, who was employed by the agency for 40 years, is suspected of stealing funds between 2002 and 2018 that were destined for projects to help disadvantaged people.
"The suspect has been arrested," prosecutor Thomas Anderskov Riis of Denmark's Serious Economic and International Crime unit said in a statement.
The woman, identified in Danish media as 64-year-old Britta Nielsen, was arrested by Johannesburg police.
"We are now asking South African authorities to decide about an extradition to Denmark," Anderskov Riis said.
Danish authorities said they had seized some of the suspect's assets believed to stem from the scam.
A man was arrested in the case in late October as he was trying to leave South Africa. His role in the case is not yet known. DM
The national flag at the Danish Parliament Christiansborg Palace on half staff as the funeral service of Prince Consort Henrik of Denmark takes place at Christiansborg Palace Church (Christiansborg Slotskirke) in Copenhagen, Denmark, 20 February 2018. The 83-year-old French-born prince died at Fredensborg Castle on 13 February 2018. EPA-EFE/Jens Noergaard Larsen DENMARK OUT