The woman, who has been identified as 28-year-old Urmila Sharma, gave birth to what appears to be a baby girl with two heads.
She also has two necks and two spines and share one body, which makes it impossible for doctors to separate the twins. Doctors are concerned she may not survive more than a few days.
New York Daily News reports Sharma and her husband couldn't afford to have an ultrasound earlier in the pregnancy to check for complications so they had no idea she was carrying the twins.
A doctor told the Daily Mail they didn't find out until two weeks before giving birth and by then it was too late to do anything.
The baby is currently being treated in intensive care.