Toshia Edmonson was in serious-but-stable condition at Methodist Dallas Medical Center following the early Saturday stabbing, the Dallas Morning News reported.
The girl was being held at a juvenile facility after being charged with family violence aggravated assault with a deadly weapon, the newspaper said.
The name of the 11-year-old girl and her relationship to the victim had not been released, the newspaper said.
"It's family violence. That's all I can say," police spokeswoman Monica Cordova said.
Police said the girl told officers she was upset that she had been brought home about 11:45 p.m. Friday. She allegedly said Edmonson shoved her into a sofa and threatened to "give her away."
A police reported stated after Edmonson went to sleep, the girl got a knife from the kitchen and stabbed her in the head, neck and shoulder, the newspaper said.
Edmonson was able to gain control of the knife and another person in the apartment summoned help.