"It's your birthday -- one of my favorite people on the planet," Shriver says in the clip. "I love you, I admire you, I enjoy you, I like you and I can't wait to celebrate with you!"
Kotb adopted Haley Joy in February 2017, and is raising her daughter with boyfriend Joel Schiffman.
She previously expressed her surprise and gratitude in an interview with People in May ahead of Mother's Day.
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"I still have moments now where I wake up in the middle of the night and look over at Joel and think to myself, 'Oh my God. I have a baby in the other room.' I can't even believe that it's really real," the star said.
"Imagine living your whole life one way, and then suddenly everything changes and you can't believe that you get to do that," she explained.
"I've dreamed of it, but I didn't think it would happen, so on Mother's Day, it's underscored."
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