"I am concerned that the attention caused by this allegation has created a distraction for the gallery's board and staff and, out of respect for them and the institution, I believe that this is the right thing to do."
The complaint was laid by a woman who worked with Burke at the Mendel Art Gallery, which was now known as Remai Modern, CBC News said.
Burke had previously told CBC News the allegation had been "incorrectly characterised in media reports".
"I am aware of an unproven allegation against me that dates back to 2013 and was filed in 2016," Burke said.
"I continue to co-operate fully and engage actively in the process."
Burke had earlier spent more than 20 years working in art museums across New Zealand and Canada.
Chris Brooks, chief executive of Regional Facilities Auckland and acting director of Auckland Art Gallery Toi o Tāmaki said they had accepted Burke's decision and wished him the best for the future. They were now recommencing the search for a new gallery director.
Brooks previously wouldn't confirm to the Herald how his team heard about the reported investigation or whether or not they knew about it before Burke was hired.
CBC previously said it had obtained a document showing the complaint had been filed to Saskatchewan's Human Rights Commission but that the document didn't detail the specifics of the allegation.
The commission's investigator Lewanna Dubray wrote in the document that her aim in investigating the complaint was to determine the facts and gather information.
Dubray was seeking information from the complainant, Burke and "all potential witnesses".
New Zealander Burke has worked as director of the Govett-Brewster Art Gallery in New Plymouth and assistant director of the Wellington City Art Gallery.
He also spent three years at the Arts Council of New Zealand.
He left New Zealand in 2005 to run the Power Plant in Toronto "where he increased visitation by more than 250 per cent and, in partnership with Sotheby's NY, initiated the most successful fundraising event in the gallery's history", according to an Auckland Art Gallery release.
In his most recent role as chief executive of Remai Modern, Burke oversaw a $180 million fundraising campaign and construction of a new art museum building.
"Under Gregory's leadership, Remai Modern attracted over 450,000 visitors in its first year of operation," Auckland Art Gallery chief executive Chris Brooks said in a media release on Burke's appointment.
This was "240 per cent more than anticipated in a city of only 300,000 people, with 40 per cent of visitors from outside the region."
