The former Britta Hanson, 21, married Palin's 22-year-old son, Track, in May.
People.com said a friend from the couple's native Alaska announced the baby news and posted pictures of the expectant mother on Facebook.
Britta is a nursing student and Track is an Army Reservist and commercial fisherman.
Sarah Palin is a former governor of Alaska and 2008 GOP vice presidential nominee. Sarah's teenage daughter Bristol was pregnant with her first child during the 2008 presidential election. She became a celebrity by speaking publicly about teen pregnancy, competing on TV's "Dancing with the Stars" and writing a memoir.
The family did not respond immediately to a request for comment on the news of Britta's pregnancy, People.com said.