The meeting with Tutu, an anti-apartheid icon, was at Cape Town's 55,000-seat soccer stadium built for the 2010 World Cup.
Obama talked about HIV/AIDS prevention and urged youth to exercise and participate in sports. She was accompanied by her daughters, Malia and Sasha, and her niece and nephew, Leslie and Avery Robinson, the children of her brother, Craig.
"The solution lies with all of you, because if you all figure this out and you're able to talk about these issues and you're able to ask for help, and you're able to pass on good information to maybe even your parents and your friends and your community and those younger than you, that's how we fix this problem.
"So that's another thing that young people can do. You all can stop the trend and start a new road to better information," the first lady said.
Obama continues her weeklong trip to southern Africa in neighboring Botswana.
Earlier, the first lady met with high school students in Cape Town, although a visit to infamous Robben Island was canceled because of bad weather.
"Whenever I travel as first lady, my priority is to meet with young people like all of you because No. 1, you are beautiful and handsome and really cool," Obama told the University of Cape Town audience of students selected from high schools in nearby townships. "Every time I visit with young people I come away inspired."
Attending college requires a willingness to work hard, she said.
Aides said Obama and her family were looking forward to the trip to Robben Island to visit the cell where former South African President Nelson Mandela was held for part of the 27 years he was imprisoned. The trip was canceled because of high winds and rough waters.
Instead she toured the District Six Museum, which memorializes the history of a Cape Town sector established in 1870s as a racially mixed area then forcibly segregated in the 1970s. Non-whites were removed to outlying areas.