Three people have already been charged in the extraordinary fraud case in which Nielsen swindled the state out of 111 million kroner over a 16-year period.
She is also being investigated for suspicious transactions going back as far as 1997. She worked at the Socialstyrelsen social authority for 40 years.
An official request for her extradition to Denmark has been lodged with the South African authorities.
Nielsen is the second person arrested in the case following the detainment of a man at the main airport in Johannesburg last week.