The exchange occurred during an episode of the Facebook Watch show "New Mom, Who Dis?" posted on Wednesday.
"Why did you paint your face brown?" a girl standing with her twin sister asked Trudeau.
"Ooh, it was something I shouldn't have done because it hurt people," he said. "It's not something that you should do and that is something that I learned. I didn't know it back then but I know it now -- and I'm sorry I hurt people."
Trudeau apologized last month for wearing brownface makeup to an "Arabian Nights" party at the private school where he was teaching in 2001, saying, "I should have known better."
A photo showed Trudeau, then the 29-year-old son of the late former Prime Minister Pierre Trudeau, clad in a white turban and robes with his face, neck and hands darkened significantly.
Wednesday's episode, hosted by Canadian TV personality Jessi Cruickshank, showed the girl following up by asking Trudeau whether he painted both his hands and nose brown. "Yeah and it was the wrong thing to do," the prime minister responded.
"And I had a good conversation with my kids around taking responsibility for my mistakes and making sure that we're always sticking up for each other and not teasing each other and being respectful towards each other.
"And I'm sorry that I hurt you as well. I'm sorry that I hurt kids who ... face teasing and discrimination because of the color of their skin. That's just not right in this country or anywhere around the world. We all have to work together to make sure that that doesn't happen."
Fox News' Morgan Phillips contributed to this report.