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The 2001 yearbook picture obtained by Time Magazine shows Mr Trudeau with skin-darkening make-up on his face and hands at the West Point Grey Academy.
Addressing the image, Mr Trudeau said he "deeply regretted" his actions and "should have known better".
The prime minister is battling for re-election on 21 October.
Mr Trudeau, son of the late former Prime Minister Pierre Trudeau, was 29 when he took part in the gala at the school in Vancouver.
The image is politically embarrassing for the prime minister because he has made progressive policies a signature issue.
How did Trudeau respond?
Speaking to journalists after the Time article was published, Mr Trudeau said he had dressed up in the photo in an Aladdin costume at an Arabian Nights-themed gala.
"I take responsibility for my decision to do that. I shouldn't have done it.
"I should have known better. It was something that I didn't think was racist at the time, but now I recognise it was something racist to do and I am deeply sorry."
When asked if there had been other occasions, Mr Trudeau told reporters he had also worn make-up when he was a student performing at a talent show in high school.
An image from that incident has since been posted to Twitter.
A source has confirmed to the BBC that the image is indeed from the second incident Mr Trudeau referred to.
He wore "blackface" and sang Day-O, a Jamaican folk song popularised by American civil rights activist Harry Belafonte.
What is 'brownface'?
Like "blackface", "brownface" typically refers to when someone paints their face darker to appear like someone with a different skin colour.
The practice is associated with minstrel performances - in past centuries, white actors could be seen with their faces painted black, caricaturing African-Americans, and perpetuating offensive and racist stereotypes.
In recent years, there have been several controversies involving politicians, celebrities and brands accused of "blackface", "brownface" or "yellowface".
On Wednesday, Mr Trudeau said "brownface" was "a significant thing that is very hurtful" to "communities and people who live with intersectionalities and face discrimination".
Mustafa Farooq, executive director of the National Council of Canadian Muslims, said: "Seeing the prime minister in brownface/blackface is deeply saddening. The wearing of blackface/brownface is reprehensible, and hearkens back to a history of racism and an Orientalist mythology which is unacceptable."
The council added that it recognised "people can change and evolve over two decades". Later, the council issued a tweet thanking Mr Trudeau for apologising promptly.
What's the political reaction been?
The picture was racist in 2001 and is racist now, said Andrew Scheer, leader of the opposition Conservatives.
"What Canadians saw this evening is someone with a total lack of judgement and integrity and someone who is not fit to govern this country," he said.
New Democratic Party leader Jagmeet Singh, a Sikh, said the image was "troubling" and "insulting".
"Any time we hear examples of brownface or blackface, it's making a mockery of someone for what they live and what their lived experiences are," Mr Singh told journalists on the campaign trail in Toronto.
The image was also criticised in a tweet by Green Party leader Elizabeth May.
Contradicting his brand
Analysis by Jessica Murphy, BBC News, Toronto
It is still too early to say how damaging this will be for Justin Trudeau but there is no doubt his tough fight for re-election just got tougher.
Canadians have made clear that they pay attention when Mr Trudeau does something that contradicts his progressive political brand.
He will also have to explain himself further to the many Canadians from diverse backgrounds who may feel deeply hurt by the image.
Jagmeet Singh - who has spoken openly about the racism he faced in Canada growing up - wrote online that this is "not about the prime minister".
"This is about every young person mocked for the colour of their skin, the child who had the turban ripped from their head."
Brian Lilley, a political columnist for the tabloid Toronto Sun, said it was a "shocking photo" and that Mr Trudeau was "a hypocrite".
"Trudeau isn't resigning over this even though he would demand that any other party fire any candidate caught in the same situation," he said.
Meanwhile, political scientist Max Cameron told the Vancouver Sun that Mr Trudeau's apology "hit all the right notes", but had still caused "a real dent in the strongest part of his armour" as he had built himself up as a defender of multiculturalism and tolerance.
Analysing the fallout, weekly news magazine Maclean's said, "Blackface has a long, troubling history in Canada."
However, Dr Cheryl Thompson, who has researched the phenomenon in Canada, told the magazine it "was not nearly so widely denounced in 2001 as it is now".
She credited Mr Trudeau for apologising unequivocally but said she hoped his colleagues would not "let him off easily".
Mr Trudeau has taken a pro-immigration stance as prime minister, and worked to appeal to ethnic minority voters.
However, his costume choices have attracted criticism in the past - including during a 2018 official visit to India, when his extensive range of traditional Indian outfits were mocked as "ridiculously overdressed".
Opinion polls indicate October's election will be a tough race for Mr Trudeau who is seeking a second term in office.
His campaign got off to a bad start after his plane was grounded by a scraped wing on the first day. A bus ferrying journalists collided with the wing of the Liberal party's chartered Boeing last week.
Earlier this year, in the US, Virginia governor Ralph Northam faced calls to resign over a photo in his 1984 yearbook.
The photo showed a person in blackface beside another in Ku Klux Klan robes.
Mr Northam initially apologised for the photo - but later said he was neither of the men pictured.
However, he said he had worn blackface on a separate occasion that year while dressing up as Michael Jackson.
