Gundeep Sanghera, 37, pleaded guilty at Bradford Crown Court to the manslaughter of Amrita Kaur on the grounds of diminished responsibility.
Wheelchair-bound Sanghera sobbed audibly into a tissue throughout the hearing as the court heard how she killed Amrita when she jumped out of a first-floor window in a suicide attempt.
It is not known whether Sanghera threw her daughter from the window before jumping herself, or if she jumped with the girl.
The court heard that Sanghera was suffering from paranoid schizophrenia at the time of the killing and believed that someone was coming to take Amrita and torture her.
Sophie Drake, prosecuting, said the defendant also believed that Islamic terrorists were using satellites to monitor her and were coming into her home.
The court heard that Sanghera suffered from memory loss about the incident in February last year and cannot remember how she or her daughter came to be outside the house in Delamere Street, in Bradford.
Judge Jonathan Durham Hall QC said: “This is a tragic matter Gundeep Sanghera and you have pleaded guilty, without prevarication and clearly at the earliest opportunity, to the unlawful killing of another person. That person is your 22-month-old daughter Amrita, who you loved deeply and you will never recover from this.”
Judge Durham Hall sentenced Sanghera to a hospital order with an indefinite restriction order on her release.
He said: “The doctors in this case unanimously come to the conclusion that you were very seriously poorly at the time.
“At the material time, you were in the grip of the severe symptoms typical of schizophrenia, with persistent delusions, including a belief your daughter was to be taken and tortured. A very grave delusion that must have affected you.”
He added: “It is necessary for the protection of the public from serious harm to impose a restriction on your release.
“Everybody I know will be working to achieve your recovery and to assist you to cope with the dreadful and tragic actions that unfolded on the 18 February 2014.”
The court heard that Sanghera was of “impeccable” character before this incident.
Michelle Colborne QC, defending, said: “This case is a tragic one and Gundeep Sanghera is a lady of impeccable character.”
She added: “There was nothing in her background to suggest she would ever behave in a volatile and dangerous manner.”
Ms Colborne said Sanghera was the victim of domestic violence and moved to Bradford with Amrita in 2012 seeking refuge.
She said everyone involved with the mother described her as “exemplary”.
“She nurtured and was devoted to her child,” Ms Colborne said.
Detective Superintendent Jon Morgan, of West Yorkshire Police, said: “Sanghera was battling with mental health issues and the circumstances surrounding these sadly resulted in the death of her child and her suffering life-changing injuries.
“The family members affected have acted with dignity throughout and supported the investigation.
“Our thoughts are now with them at this difficult time.”