TLC says the child is in stable condition at the University of Arkansas for Medical Sciences in Little Rock.
The network airs the show starring Duggar, her 44-year-old husband and their brood. It says the Duggars named their 19th child and ninth daughter Josie Brooklyn. The Duggars' first grandchild was born Oct. 8.
The family lives in a 7,000-square-foot house in Arkansas, where they manage commercial real estate property. The couple has said they'll continue welcoming children as long as Michelle is able to have them.