Officers said the mother, Taheerah Ahmad, is suspected of committing the stabbing and starting a fire in the home.
A 9-year-old child said Ahmad duct-taped the hands of the children, put socks in their mouths and stabbed the 11-year-old, according to police. She then reportedly burned her phone, setting the kitchen on fire, and left the scene. Officers said the 9-year-old was able to flee to a relative's home.
After police took Ahmad into custody, they said she claimed she stabbed the 11-year-old victim in self-defense. She reportedly told officers she bound the 9-year-old and 11-year-old earlier in the evening for "reading their books," and police said she claimed the older child broke away and attacked her, prompting her to stab the child at least 50 times.
Police said they recovered two knives and a gardening tool from the scene. They reportedly believe she set the house on fire to make sure the child died.
Police initially said that Ahmad had taken her 7-year-old daughter with her when she fled, but they later clarified that the child was eight years old.
Tulsa police issued an Amber Alert.
Officers brought Ahmad into custody after someone spotted her in a downtown Tulsa parking lot. They said they believe she had been sitting in the parking lot for some time before she was spotted.
The victim is in critical condition after undergoing surgery.
Police said the father of the children is in Tennessee and did not know where the suspect was during the investigation.
Ahmad faces charges related to assault and battery with the intent to kill, arson and child neglect.