Farmer Omprakash Yadav and his wife Phoolmati Devi, from Koria in north Indian state of Chhattisgarh, had no idea their daughter had any abnormalities before she was born.
Doctors said apart from having no arms and legs the little girl is healthy, and the parents have pledged to "accept her as she is".
Dr GD Baghel of Baikunthpur district hospital said: "The baby is doing well.
The baby is healthy but was born without arms or legs
"She weighs like any normal kid and has all her vital organs working properly just that she doesn't have any limbs.
"But I am sorry to say this but there is no cure of this condition."
The yet-to-be-named baby was born at home before being taken to hospital, last week.
The parents were told their daughter was healthy before she was born
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I am happy to be blessed with a baby
Mr Yadav, a farmer, said: "I don't know how to react to this.
"I am happy to be blessed with a baby, but my happiness turns into a gloom when I try to think up what will be her future."
His wife added: "The midwife told me that everything was normal.
The baby's father said he was 'blessed' to have a baby
"I was told that it was a girl and that she was good, normal, healthy.
"I gave birth in the middle of the night and was told the next afternoon about the condition of my baby.
"I was surprised. You just have to accept her as she is."