In government

She was elected to parliament in the 1993 election in which the Liberal party won all but one of the 99 Ontario seats. Although the former Liberal candidate ran against her as an independent, she defeated New Democratic Party (NDP) incumbent Neil Young by a margin of two-to-one, thus becoming the first Liberal in history to represent the Beaches area south of the Danforth. As of 2008 she has been re-elected five times easily defeating high-profile candidates such as Peter Tabuns (2004 election, by 7,738 votes)^[7] and Marilyn Churley (2006 election, by 2,778 votes;^[3] 2008 election, by 4,092 votes^[8]).

On August 3, 1999, Minna was appointed to Cabinet as the Minister of International Cooperation. She held the post until the beginning of 2002. On December 11, 2001, Minna was accused of improperly voting in a municipal by-election. She voted for friend and colleague Gail Nyberg who was running to replace Michael Prue who had been elected to the Provincial government in a September by-election. On advice from municipal officials, Minna cast a ballot even though she didn't live within the ward which occupies the northern half of her riding. According to municipal election rules, anyone who owns or rents a business is allowed to vote. Minna's constituency office was in the ward so that allowed her to cast a ballot.^[9] Soon after, Minna was dropped from Cabinet during a ministerial shuffle.

Minna was bitter about the demotion and complained to the Liberal Party's women's caucus that she was told to keep quiet about the issue. She claimed she was "hung out to dry by ambitious individuals...."^[10] Later she conceded that the PMO's office had told her that it would be better to wait for the results of the ethics investigation. Initially the ethics counsellor terminated the allegations probe since she was dropped from Cabinet but Minna insisted that it be reopened. She said, "It's my personal credibility that's at stake. It's not the cabinet post." Fellow Liberal MP Sheila Copps who sympathized with Minna's situation was quoted as saying, "The one thing you have in politics is your reputation."^[11] The probe was reopened and she was subsequently cleared of any wrongdoing.^[12]

During her time in government, Minna has held several leadership roles that have focused on immigration and international relations. In 1994 she was appointed Vice-Chair of the Standing Committee on Human Resources Development and served as Parliamentary Secretary to the Minister of Citizenship and Immigration from 1996 to 1998. In October 2004, Minna was appointed special adviser to the Minister of Foreign Affairs on issues of women, peace and security. In March 2005, Minna led a five-person Parliamentary delegation to assist with the peace process in Sri Lanka.^[2]

In opposition

From 2006 to January 2009, Minna was the Official Opposition Critic for the Status of Women.^[13] Minna was the Official Opposition Critic for Labour.^[14] On May 2, 2011, during the 41st federal election, Minna lost her seat to NDP candidate Matthew Kellway.^[15]