Malik Obama, 52, told a Kenya news station that the teen quit school and wanted to get married. He appeared on video taken by a hidden camera, although he knew he was talking to journalists.
"She decided she doesn't want to go back to school. She wants to get married now. She came here, and what am I supposed to do? So we are married," Malik Obama said on the video broadcast by NTV.
Sheila Anyango is now Malik Obama's third wife, although he did not say when the wedding took place. Polygamy is legal in Kenya if it falls under religious or cultural traditions.
The 19-year-old's mother told The Associated Press on Friday she is furious that her daughter quit high school and married the 52-year-old. Mary Aoko Ouma says her daughter tried to marry Malik Obama two years ago, but the mother says she wouldn't give permission.
Ouma said she has struggled to send her six children to school since her husband died in 1996, and that she was severely disappointed Anyango didn't finish. Ouma said Anyango was setting a bad example for her other daughter who is still in high school.
"I told her not to get married until she has finished her education. Let the world teach her a lesson even if she has problems in her marriage. I don't want to see her again," Ouma said.
Ouma said she did not receive a bride price from Malik Obama but that if she received one she would spend it on her other children's schooling.
Jane Omogi, a district education officer in Siaya in western Kenya, said officials are investigating, but she declined to make any further comment.
Barack Obama's father had at least six other children in his native Kenya. Kenyans have claimed the U.S. president as one of their own even though he was raised by his mother and did not know his Kenyan father or relatives there well.