In videos obtained by TMZ, Obama, in a floor-length black dress with her hair down, led the bride with a smile as she said, "I promise to stand next to and support you through all of life's trials and trails."
Tina Newman, who posted the since-deleted Instagram Story, wrote, "Holy Moly" and "That moment when Michelle Obama officiated at your [cousin's] wedding!"
The family has strong ties to the Obamas. Rivkin's father is Robert S. Rivkin, the deputy mayor of Chicago, and her mother was appointed by former President Barack Obama to serve as Director of the President's Commission on White House Fellowships.
The newlyweds met in high school and both graduated from Yale, according to The New York Times.
A guest at the wedding posted photos of the celebration on Instagram, showing the couple dancing and highlighting the stunning setting, Theater on the Lake.
Mrs. Obama is keeping busy in her post-White House years: She is embarking on a 10-city book tour in November and December to promote her upcoming memoir, Becoming, in Chicago, Los Angeles, Washington, D.C., Boston, Philadelphia, Brooklyn, Detroit, Denver, San Jose and Dallas.
"Over this time that I've been out of the White House, I've had time to think and reflect for the first time in a long time. I spent some time really thinking about the people, the stories and the experiences that have shaped me and helped me become the person I am today," Obama said in a video about her book.
She continued, "I am proud of what I've created. I'm proud because it is candid, it's honest, it is totally and utterly me. So I'm also a little frightened because it is so candid and honest and open."