Britta, 21, married Palin's 22-year-old son Track in May.
Their first child was born Sunday, UsMagazine.com reported.
No other details regarding the baby's birth were immediately available.
Britta is a nursing student. Track is an Army reservist and commercial fisherman.
Sarah Palin was the 2008 Republican vice presidential nominee. Her teenage daughter, Bristol, was pregnant with her first child during the 2008 presidential election and became a celebrity by speaking publicly about teen pregnancy, competing on TV's "Dancing with the Stars" and writing a memoir.