Time magazine published the photo, saying it was taken from the yearbook from West Point Grey Academy, a private school in British Columbia where Mr Trudeau worked as a teacher before entering politics.
It depicts the then 29-year-old wearing a turban and robe, with dark make-up on his hands, face and neck.
Mr Trudeau, who launched his re-election campaign a week ago, apologised and begged Canadians to forgive him, adding that he should have known better.
"I'm pissed off at myself, I'm disappointed in myself," the prime minister told reporters travelling with him on his campaign plane.
The PM is the latest politician to face scrutiny over racially insensitive photos and actions from their younger days. Earlier this year, Virginia governor Ralph Northam faced intense pressure to resign after a racist picture surfaced from his 1984 medical school yearbook page.
He denied being in the picture but admitted wearing blackface as a young man while portraying Michael Jackson at a dance party in the 1980s.
Since then, Virginia attorney general Mark Herring has acknowledged wearing blackface in college, and Alabama governor Kay Ivey has publicly apologised for donning blackface during a college skit more than 50 years ago. None has resigned.
The photo of Mr Trudeau was taken at the school's annual dinner which had an Arabian Nights theme, he said, adding that he was dressed as a character from Aladdin.
The prime minister said it was not the first time he had painted his face, as he had once performed a version of Harry Belafonte's Banana Boat Song (Day-O) during a talent show.
"I should have known better then but I didn't, and I am deeply sorry for it," Mr Trudeau said.
"I'm going to ask Canadians to forgive me for what I did. I shouldn't have done that. I take responsibility for it. It was a dumb thing to do."
He said he has always been more enthusiastic about costumes than is "sometimes appropriate".
"These are the situations I regret deeply," he added.
The prime minister, who champions diversity and multiculturalism, said he did not consider it racist at the time but society knows better now.
Mr Trudeau has been admired by liberals around the world for his progressive policies in the Trump era, with Canada accepting more refugees than the US. His Liberal government has also strongly advocated free trade and legalised cannabis nationwide.
But the 47-year-old son of late prime minister Pierre Trudeau was already vulnerable following one of the biggest scandals in Canadian political history, which arose when his former attorney general said he improperly pressured her to halt the criminal prosecution of a company in Quebec.
Mr Trudeau has said he was standing up for jobs, but the scandal rocked the government and led to multiple resignations earlier this year, causing a drop in the leader's poll ratings.
After the release of the brownface photo, Mr Trudeau said he would talk to his children about taking responsibility.
His quick apology did not stem the criticism from political opponents, who took the prime minister to task for what they said was troubling behaviour.
"It is insulting. Any time we hear examples of brownface or blackface it's making a mockery of someone for what they live, for what their lived experiences are. I think he has to answer for it," said New Democrat leader Jagmeet Singh, a Sikh who wears a turban and the first visible minority to lead a national party.
Andrew Scheer, the opposition Conservative leader, said brownface was racist in 2001 and is racist in 2019.
"What Canadians saw this evening was someone with a complete lack of judgement and integrity and someone who is not fit to govern this country," he said.