Fialkowska was born in Montreal, Quebec, to a Canadian mother (Bridget Todd Fialkowski) and a Polish father (Jerzy Fialkowski), an engineer and Polish army officer who emigrated to Canada in 1945. Her mother, Scottish-Irish and Cree descent, studied piano in the class of Alfred Cortot at the École Normale de Musique de Paris (1935–1939). Fialkowska is the granddaughter of John Todd, Canada's first professor of parasitology, and great-granddaughter of Edward Clouston, President of the Canadian Bankers Association. She is the cousin of former Canadian cabinet minister David Anderson and cousin of stage and screen actor Christopher Plummer.