A judge at Manchester County and Family Court ruled yesterday that the child, who will turn two this year, is at risk because religious and cultural pressure had overridden her mother's "maternal instinct".
Social workers in the UK believe three other girls from the family, which cannot be named for legal reasons, had been subjected to a similar procedure.
Female genital mutilation (FGM), also known as female circumcision, involves ritual intimate cutting, sometimes without anaesthetic, and has been banned in the UK.
Judge Robert Jordan made an "FGM protection order" in Manchester after a private family court hearing, 'Manchester Evening News' reported.
The judge was told that the baby's three older sisters had previously been taken to India so that FGM could be carried out on them. He made the protection order after concluding that the little girl was also at risk and needed protecting.
"The effect of the cultural pressure overrode the mother's maternal instinct. As a consequence of religious and cultural pressure the mother facilitated the mutilation of her children," he noted.
FGM protection orders came into force in Britain three years ago and give police and local authorities power to intervene to prevent such procedures. Parents can be barred from taking children abroad and passports can be seized and face prosecution if they breach it.
According to UK research, FGM is less common in India and is more prevalent in around 28 African countries and in parts of the Middle and Far East.
In Britain, communities that have been identified as at risk of FGM include Somali, Kenyan, Ethiopian, Sierra Leonean, Sudanese, Egyptian, Nigerian, Eritrean, Yemeni, Kurdish and Indonesian women and girls.
It is believed to be a way of ensuring virginity and chastity and is used to safeguard girls from sex outside marriage and from having sexual feelings.
Although FGM is practised by secular communities, it is most often claimed to be carried out in accordance with religious beliefs.