The foetuses were found to be at 8 to 10 weeks of gestation.
Each foetus had four limbs, a spine, rib cage, intestines, primitive brain tissue, anus and an umbilical cord connected to a single placenta-like mass.
One of the foetuses weighed 14.2 grams and the other, 9.3 grams.
Doctors had to perform a surgery on the baby girl at three weeks to remove the foetuses. The girl was discharged from the hospital eight days following the surgery.
The condition was revealed to be an abnormality called the 'fetus in fetu' condition.
Dr. Nicholas Chao, one of the surgeons who operated on the baby, said, reported CNN: "[It's] one of those very rare things that make the world stand still."
'Fetus in fetu' affects 1 in 500,000 births globally and less than 200 cases have been reported in literature, according to a study published by Chao and his colleagues this month in the Hong Kong Medical Journal.
"It was almost impossible to detect during the prenatal check-up, as the embryo inside the baby was too small," said Dr. Yu Kai-man, a specialist in obstetrics and gyneacology.
"Since it is impossible for the little girl to have conceived the pregnancy on her own, the fertilization of the twin fetuses, of course, belongs to her parents, which has gone to the wrong place."
While the exact factors leading to the 'fetus in fetu' abnormality remain unknown, the World Health Organisation has classified the condition a variant of mature teratoma, a type of cancer.
"There are controversies over what these things really are ... [there's] not enough hard scientific data to prove either one because of the limited cases. You need a big series of these cases and lots of observations to get a more scientific understanding," said Dr. Chao.