The find has been hailed as one of the most important discoveries to date in the field of human evolution.
Scientists believe the remains offer a remarkable opportunity to study growth and development in an important extinct human ancestor.
The baby girl’s fossilised bones were first discovered in 2000 in Dikika in Ethiopia’s Awash Valley.
The best-known Australopithecus afarensis was nicknamed Lucy after her adult skeleton was found in 1974.
Lucy’s baby has been named Selam, which means "peace" in several Ethiopian languages, scientists wrote in the British journal Nature.
The child’s bones were locked inside a block of sandstone and it has taken five years to remove the skeleton and skull.
Scientists say Selam was probably buried shortly after a flood in what was then a delta region, river by streams that flowed into a lake.
Selam was found on the opposite bank to where Lucy and other Australopithecus afarensis remains were found.
Dating of the sediment in which her bones were found suggests the child lived between 3.31 and 3.35 million years ago.
The remains consist of a whole skull, the entire torso and parts of the upper and lower limbs.
CT scans reveal unerupted teeth in the jaw which makes scientists think that the bones were that of a young child.
Remarkable find
Ethiopian scientist, Zeresenay Alemseged, from the Max Planck Institute in Leipzig, eastern Germany, made the discovery.
Fossil is still being extracted but Alemseged's team believes it has found something unique in palaeontology.
The fragile bones of infants rarely survive long enough to become
fossilised.
Researchers say the skeleton has strongly curved finger bones which suggest a hand structure designed for climbing trees.
A final pointer to ape-like characteristics is the presence of a tiny throat bone, the hyoid.
It’s hoped the girl’s remains will shed light on a hotly disputed branch of the human tree known as Australopithecus afarensis.
Once thought by some to be our ancestor, Australopithecus afarensis is now widely considered to be a failed branch of the human tree.
For more than 20 years, Lucy has remained the earliest known member of the hominid family.
Hominids are primates who split from apes between five and seven million years ago.
They are considered the forerunners of anatomically modern humans, who appeared on the scene about 200,0000 years ago.
The exact line of geneaology of the small, rather ape-like creatures remains unclear.
Many experts suspect the hominid was anatomically far closer to apes than humans.
Its brain was not much larger than that of a chimpanzee.
However it no longer had the large canines that distinguished apes from hominids, although it had relatively large chewing teeth that were still primitive.
The other comparably complete infant hominid skeleton in the fossil record is that of a Neanderthal child who lived less than 100,000 years ago.