Jordan Brown is alleged to have shot the woman in the back of the head and then got on a school bus and went to class in Pennsylvania.
The youngster has been charged as an adult because state law allows prosecutors to charge children as young as 10 with criminal homicide.
But a prison warden says he will ask a judge to move the boy from an adult facility to a juvenile detention centre because the jail cannot accommodate the child.
Lawrence County Warden Charles Adamo says the jail, which houses about 300 prisoners, cannot offer proper long-term care for Brown.
The young suspect is accused of killing 26-year-old Kenzie Marie Houkwho with a shotgun, which apparently belonged to him.Authorities said the model 20-gauge shotgun was thought to have been found in the boy's bedroom.
It is designed for children and such weapons do not have to be registered.
"Designed for children"?!? It's cases like these that makes me shake my head at all the gun nuts and 2nd Amendment enthusiasts out there. Call me insane, but what rational reason is there for an 11-year-old kid to be owning a gun? I mean, when will people stop making it about politics and realize that the sheer stupidity of some of our nation's guns laws are in turn, killing lots of innocent people?