Duggar told his 500,000 Instagram followers that his fourth child, Meredith Grace Duggar, was born weighing 7 pounds, 14 ounces. Duggar said the baby and mom, Anna Duggar, are doing well. Duggar's other children are Mackynzie, Michael and Marcus.
The comments on the photo range from words of support and congratulations to those using the hashtag, "#JailJoshDuggar." In May reports surfaced that Josh Duggar, 27, had molested his sisters and others as a teenager. He has never been arrested or charged in connection with the allegations.
PHOTOS: Duggar family through the years
After being pulled from the air in May, the show was officially cancelled last week, when TLC announced it would no longer air the show.
Jill and Jessa Duggar, two of the sisters Josh Duggar touched inappropriately, will participate in a documentary to raise awareness of child sexual abuse that will air on TLC.
The Associated Press contributed to this report.