"I should have known better then, but I didn't and I did it and I'm deeply sorry," Trudeau told reporters on his campaign plane in Halifax, Nova Scotia, after Time magazine published the image.
The image of a 29-year-old Trudeau with his face in dark make-up is a major challenge for a leader who often speaks about the need to fight racial discrimination and who has three prominent ministers of Indian descent in his cabinet.
Time said the image was provided by Vancouver businessman Michael Adamson earlier this month.
Adamson was part of the West Point Grey Academy community where Trudeau worked at the time, the magazine said.
The picture was in the Vancouver private school's yearbook.