"Despite the heroic efforts of determined keepers, veterinarians and animal health technologists, the baby slipped into a coma at 3 p.m. and did not recover," said a statement on the zoo's website.
"They did everything humanly possible and then some to help keep this little elephant alive. Unfortunately, nature makes its own choices."
The three-week-old Asian pachyderm's activity levels had decreased in recent days, and she had been having problems eating and sleeping after she began teething.
Elephant calf struggles to walk in her first week.
- FROM NOV. 25, 2004: Baby elephant at risk after mother's rejection
The unnamed calf's 14-year-old mother Maharani didn't want anything to do with her soon after her birth, leaving her to the care of zookeepers, who hand-fed her with a special formula.
But the formula didn't have the same nutrients and antibodies that would be available in the mother's milk.
Since she was born in mid-November, the baby had already overcome an infection which required a blood transfusion from two female elephants.
Zoo spokesperson Trish Exton-Parder says it has received calls from around the world by those concerned about the elephant.
The zoo had established a trust fund to help pay for the elephant's care, which cost about $500 a day, including antibiotics, special formula, lab tests and medical supplies.
Orphaned elephants usually have a 50 per cent chance of survival.
