The surprise resignation comes eight months into the Royal Commission into Child Sexual Abuse, which began in Sydney in September.
The main aim of the Royal Commission is to investigate systemic failures within church and state-run institutions relating to child sexual abuse and related matters.
Last year, former Prime Minister Julia Gillard announced the terms of the Royal Commission.
Ms Dines, a former public servant of 20 years, was apppinted to the role in late 2012.
She had previously coordinated the Commonwealth’s representation before the 2011 Queensland Floods Commission of Inquiry, as well as the 2009 Victorian Bushfires Royal Commission.