St. Clair County Sheriff Terry Surles said the victim, Katelynn Arnold, was discovered Thursday night outside her home in Ragland, some 40 miles northeast of Birmingham.
The child was taken to St. Clair Regional Hospital, where she was pronounced dead, he said.
Citing laws covering juveniles, Surles would not identify the suspect. A hearing has been set to decide whether he will be certified as an adult.
St. Clair County District Attorney Richard Minor told CNN the suspect was charged in juvenile court with one count of murder and that the charging documents are sealed.
Both children lived with foster parents at the home where the body was found, Surles said.
It was not clear whether they were related to the foster family, he said. “We’re trying to find out who’s related to who,” Surles said.
Asked what the motive may have been, he said, “I have no idea.”
But he said he had no doubt that the killing was no accident. “That’s why he’s charged with murder,” he said.
The victim’s foster mother found the child in the yard after having searched for her by driving around the neighborhood, he said. “This child was actually touching the ground; it wasn’t as if she was dangling on from a tree limb.”
Surles said the cotton rope had been tied to a limb in a figure-8 knot, not a noose. “That rope apparently had been used for an old tire swing and I think during a storm last year the tree got blown down. The rope was readily available.”
The boy was taken into custody Thursday night, Surles said.
Neighbors had seen the children in the yard earlier in the day, he said.
St. Clair County Coroner Dennis Russell said the cause of death was ligature strangulation. He has ruled the case a homicide, he said.