In a video shared on social media, the prime minister can be seen singing Bohemian Rhapsody by the British rock band, Queen.
The Queen was Canada's head of state, and Mr Trudeau designated 19 September a national day of mourning in Canada.
Critics accused the PM of a lack of respect - but others defended him.
Mr Trudeau can be seen in a T-shirt, leaning on a piano as Gregory Charles, a musician from Quebec and recipient of the Order of Canada, plays Bohemian Rhapsody.
He sings famous lyrics including "easy come, easy go, little high, little low", and "any way the wind blows".
But the video has drawn criticism from some Canadian commentators and members of the public.
Sources: BBC & NYCU