According to Radaronline.com, the Alaskan former Vice Presidential candidate and her family are celebrating the tiny new arrival, named Kayla Grace.
Track, 22, had tied the knot with his high school sweetheart Britta just three months ago in their hometown Hatcher Pass, Alaska.
At the time of the surprise wedding, her pregnancy had not been announced.
No further details have been released about when or where little Kayla was delivered.
Palin's oldest daughter Bristol was the first of her children to make her a grandmother, having had son Tripp at the age of 18.
The brunette - an outspoken advocate for teaching teens abstinence before marriage as a form of birth control - is famously estranged from her baby's father Levi Johnston.