The parents of the child and owner of the dog signed a waiver that allowed for the dog to be put down, the sheriff said.
The dog was identified by Parsons as a wolf-mix canine. The animal was seized by county animal control soon after the attack on the infant at the family's home in the Seminary community and had been held at a local shelter.
The baby suffered fatal injuries to her upper body and the dog attacked the child while she was laying in a bassinet, the sheriff said.
The father of the child took the baby to a Big Stone Gap hospital. After an initial evaluation, the infant was flown to the University of Tennessee Medical Center in Knoxville, where she was stabilized and later died at 4 p.m. Wednesday, the sheriff said.
County social services are continuing their investigation into the dog attack. Parsons said his office is still determining whether charges will be filed against the parents.