The Court heard that a further pregnancy would be a “significantly life-threatening event” for both the mother and child.
Mr Justice Cobb said the woman had the “same human rights” as everyone else and this was not a case of “eugenics”.
He has authorised health and council services to intervene and perform the sterilisation.
The name of the woman has not been released, to protect the identify of her children.
The Court of Protection, which rules in cases when people are unable to make decisions for themselves, heard the woman has no contact with any of her six children. All are being raised by carers.
The 36-year-old’s history was described as “extraordinary, tragic, and complex”.
Two of the children were born at home in conditions described as “unhygienic and overrun by pets”.
There is evidence that barbecue tongs were used as forceps, although this was denied.
In another birth, the woman – known only as DD – contested there was no father and the pregnancy resulted from a “tablet from a health food shop”.
Mr Cobb’s judgement said: “The ethical, legal and medical issues arising here are self-evidently of the utmost gravity, engaging, and profoundly impacting upon DD’s personal autonomy, privacy, bodily integrity, and reproductive rights.”
It said there were considerable concerns about the woman’s safety.
Doctors said the wall of her uterus was “tissue-paper thin” and likely to rupture in childbirth, leading to almost certain death of the infant.
Mr Cobb insisted: “Those who lack capacity have the same human rights as everyone else.
“This case is not about eugenics, this outcome has been driven by the bleak yet undisputed evidence that a further pregnancy would be a significantly life-threatening event.”
He has authorised a sterilisation operation, but there will be no notice given to the woman or her long-term partner, who also has learning disabilities.
Rebecca Schiller, the co-chairwoman of the human rights in childbirth charity Birthrights, said: “Taking away a person’s ability to have a child is truly draconian.
“It may be justified in extreme circumstances, but immense care must be taken to safeguard the rights of people with mental health conditions.”