KVII-TV reports the boy was found unresponsive Tuesday at his home near Clarendon after the father called 911. The child later died at a hospital.
Blackburn says there was evidence that the victim was assaulted. Prosecutor Luke Inman says the boy suffered "a horrific death."
Further details on the child's injuries were not immediately released. An autopsy was scheduled Thursday.
The Donley County Sheriff's Office early Thursday declined to release more details on Babcock, who was arrested Tuesday.
Clarendon is 50 miles southeast of Amarillo.