The singer and actress shared a close-up of the eight-week-old, her first child with fiancé Eric Johnson, on the social networking site along with the caption: "Howdy friends."
Simpson debuted Maxwell on the cover of People last month when her newborn was just four weeks old.
The Dukes of Hazzard star has publicly described Maxwell as "insanely beautiful" and declared that "motherhood is by far the best thing" she's ever experienced.
Simpson, who is set to marry Johnson in December, has also joked on Twitter about the size of her post-pregnancy breasts, openly wondering if she is "street legal".
The 31-year-old has recently become a spokesperson for Weight Watchers and is working to lose her baby weight.