Relative Colleen Jones tells the magazine the baby is fine and Bristol is "doing well." Jones is the sister of Bristol's grandmother.
The father is Levi Johnston, a former hockey player at Alaska's Wasilla High School. He has said he and Bristol plan to marry.
Palin created a stir in September by announcing the pregnancy as she prepared to accept her nomination at the Republican National Convention.
The governor's office called the birth a private family matter.