Mortensen, a longtime hockey fan, drew cheers as he unfurled the Montreal Canadiens (sic) flag and wrapped it around the best supporting actor trophy he received for his role in A Dangerous Method.
He said, "It's a very beautiful trophy and I think in order to cross the border safely I'll have to wrap it very, very carefully so I brought some very strong material with me."
The actor also thanked Canadian director David Cronenberg for taking a gamble by casting him as Austrian psychoanalyst Sigmund Freud in the drama.
He added, "I must thank first and foremost David Cronenberg for taking a chance on me. I don't think any other director would have thought of me as Sigmund Freud... It's only natural that I thank David. He is, after all, the only director who is willing to cast me at this point."
The film, which starred Michael Fassbender as Carl Jung, was also honoured for its art direction, original score, overall sound and sound editing.
Filmmaker Philippe Falardeau's drama Monsieur Lazhar was named best picture, and scooped five other trophies including best adapted screenplay.