After Malia Obama went off to Harvard University last month, her father couldn’t hold back the tears.

Barack Obama described that moment on Monday in a speech for the Beau Biden Foundation for the Protection of Children, which was named for former Vice President Joseph R. Biden’s older son, who died of brain cancer in 2015.

The former president said some kind words about Beau and his parents, Joe and Jill Biden, before talking about the joys and sorrows of watching children grow up.

“For those of us who have daughters, it just happens fast,” Mr. Obama said in a video published by WDEL, a news outlet based in Wilmington, Del.

“I dropped off Malia at college, and I was saying to Joe and Jill that it was a little bit like open-heart surgery, and I was proud that I did not cry in front of her. But on the way back, the Secret Service was all looking straight ahead pretending they weren’t hearing me as I sniffled and blew my nose. It was rough.”

Mr. Biden introduced Mr. Obama at the Wilmington Country Club in Delaware on Monday, calling him a “great friend.”

Malia, 19, took a gap year after high school and opted to attend Harvard this year, despite her father’s advice that she could get a good education even if she did not attend “some name-brand, famous, fancy school.”

Both Mr. Obama and his wife, Michelle, attended law school at Harvard.

Mr. Obama has let the tears flow in public on a number of occasions, including when he spoke shortly after the death of his grandmother in November 2008; when he thanked his campaign staff after winning re-election in November 2012; and during a speech about gun violence in January 2016.

The Obamas are likely to remain in Washington at least until their younger daughter, Sasha, 16, finishes high school. They spent $8.1 million on a home in the capital’s Kalorama neighborhood after leaving the White House.

In his speech on Monday, Mr. Obama praised the work of the Beau Biden Foundation, which is dedicated to protecting children from abuse.

“At the end of our lives, whatever else we’ve accomplished, the thing that we’ll remember are the joys that our children — and hopefully, way later, our grandchildren — bring us,” he said.

“And holding their hand, swinging them on a swing, listening to them talk about what had happened in school; simple stuff, but ultimately that’s what matters.”