Duncan announced he was stepping down after improperly advocating to a tax court on behalf of a constituent.
Cabinet members were recently asked to review their correspondence following revelations by The Canadian Press that Finance Minister Jim Flaherty had improperly promoted a business in his riding in its licence application to the Canadian Radio-television and Telecommunications Commission.
The federal ethics commissioner reiterated that such interventions by public office holders are forbidden.
Duncan said in a statement that a subsequent search by his office turned up his own improper advocacy.
"In June of 2011 I wrote a character reference letter to the Tax Court of Canada on behalf of an individual to whom my constituency staff was providing case work assistance on a Canada Revenue Agency matter," Duncan said in the statement.
"While the letter was written with honourable intentions, I realize that it was not appropriate for me, as a minister of the Crown, to write to the Tax Court."
Genevieve Salvas, the acting executive legal counsel for the Tax Court of Canada, said her office was just learning of the matter and had no immediate comment.
Duncan said he offered his resignation to Prime Minister Stephen Harper and it was accepted.
"I take full responsibility for my actions and the consequences they have brought," said Duncan.
"I would like to thank Mr. Duncan for his many contributions as minister and for his service to the people of Canada," Harper said in a release.
Duncan will continue to represent Vancouver Island North but his cabinet duties will be taken up temporarily by Heritage Minister James Moore.
The week began with Sen. Patrick Brazeau expelled from the Conservative party caucus as he was being charged with assault and sexual assault in an altercation at his Gatineau, Que., home.
Brazeau was already embroiled in a controversy over his Senate expense claims — a battle that has now expanded to include at least two other Conservative senators, Mike Duffy and Pamela Wallin. The upper chamber is conducting audits on all three senators, as well as on Liberal Sen. Mac Harb.
"After the last two weeks of witnessing the prime minister defend the entitlements of his senators and his ministers' conflicts of interest, it's good to finally see one Conservative, Mr. Duncan, actually take responsibility for his actions," Jean Crowder, the NDP critic for aboriginal affairs, said in an email.
Her colleague Paul Dewar said Harper appears to be showing an ethical double standard between Duncan and Flaherty, who both were caught in similar breaches of the conflict code.
The prime minister "felt (Duncan) was expendable, I guess," Dewar told CBC.
Harper spokesman Andrew MacDougall said different circumstances explained the differing consequences.
"Minister Duncan wrote to a judge as minister, an act Mr. Duncan acknowledged was inappropriate," MacDougall said in an email.
"Mr. Flaherty personally inserted the line specifying he was writing as the member of Parliament for Whitby-Oshawa. As was said at the time, the insertion of the signature block was an administrative error by staff."
Last month, ethics commissioner Mary Dawson issued orders against Flaherty and two Conservative parliamentary secretaries informing them that letters they wrote on behalf of constituents to the CRTC were improper because they used their positions to try to influence the decision of a quasi-judicial body.
She specifically noted that how they described themselves in the letter was irrelevant.
"Writing such a letter would be improper, regardless of whether or not you explicitly identified yourself as a parliamentary secretary," Dawson wrote to Eve Adams and Colin Carrie.
Section nine of the Conflict of Interest Act prohibits ministers from using their position to try to influence decision-making when doing so would improperly advance another person's private interests.
Guidelines issued by the Prime Minister's Office also say cabinet members should not intervene in courts or licence decisions of independent tribunals.
There are precedents for Duncan's resignation.
Jean Charest stepped down as minister of state for youth, and minister of state for sport and fitness, in 1990, after calling a Quebec judge about a case involving the Canadian Track and Field Association.
Duncan is the seventh cabinet minister to resign from the Conservative front bench since Harper came to office in January 2006, but only the third whose departure is linked explicitly to improper behaviour.
Maxime Bernier resigned in 2008 after leaving a secret briefing book at his then-girlfriend's apartment and Helena Guergis stepped down in 2010 amid allegations of criminal activity involving her husband's business — although no charges were ever laid.
Duncan, 64, has suffered from poor health and was seen as one of the Conservative government's less-accomplished advocates during the last several months of First Nations' protests.
With the prime minister having publicly committed to a new round of negotiations over treaty issues and land-claims settlements, the leadership of the Department of Aboriginal Affairs and Northern Development is likely to take on a much higher profile in the Conservative government.
"At this crucial time in First Nation, Metis and Inuit relations, the prime minister must move quickly to replace Mr. Duncan with a full-time minister, not someone whose time is split between three ministries," said the NDP's Crowder.
— With files from Jennifer Ditchburn
Also on HuffPost