Malavoy attended the Collège Marie de France, earning a bachelor's degree in philosophy. She later attended the Université de Montréal, earning a (2nd) bachelor's degree, and later a master's degree in social service, also earning a diploma in pastoral studies. She would attend the Université de Sherbrooke and work there from 1977–92, and from 1999-2006 as a teacher, vice-dean and dean of the faculty of Humanities. In the community, she worked for the Comité de protection de la Jeunesse, the Centre des Services sociaux en Estrie and for several associations promoting social equality and the Status and condition of women. She was a member for the No committee for the Charlottetown Accord in 1992. She is a member of the Parti Québécois since 1979 and was the first vice-president and national executive committee chair of the party from 2000-05.
Malavoy first entered politics in 1994 and was elected in the riding of Sherbrooke where she was briefly the Minister of Culture and Communications in the Jacques Parizeau cabinet. She had to step down from her position November 25, 1994, as it was found that she had illegally voted during the Quebec Referendum in 1980 as well as other federal and provincial elections since she was not a Canadian citizen at the time. After an eight-year retirement from politics, she was elected in Taillon in a by-election succeeding former Minister Pauline Marois. She was re-elected in the 2007 elections. After being the critic for municipal affairs during the first parliamentary session, she was named the critic for education after reports that Diane Lemieux, who held the portfolio during the spring session would retire from politics following a disagreement with Marois, who was named the PQ leader in July 2007.