Samuel David Cheney, who weighed 8 pounds, 6 ounces when he was born at Sibley Hospital, is the Cheneys' sixth grandchild, ABC News reported.
"The vice president is pleased to be a grandfather for the sixth time," spokeswoman Megan McGinn said.
Mary Cheney, 38, an executive for AOL, and her partner, Heather Poe, a former park ranger, have been together for 15 years and live in Great Falls, Va., The Washington Post said.
Mary Cheney and her family have resisted turning her pregnancy into a public debate.
"It is not a political statement. It is not a prop to be used in a debate by people on either side of an issue. It is my child," she said.
The vice president told CNN anchor Wolf Blitzer he was "out of line" when he asked Dick Cheney during an interview to comment on a Focus on the Family statement questioning the propriety of an unmarried couple having a child.
The Cheneys' other daughter, Elizabeth, has five children with her husband, Philip Perry.