Zoo officials say the calf was born five to six months early, as it was expected in February 2013.
"It's heartbreaking for all of us involved to know that this calf didn't make it," said Dr. Jake Veasey, the director of animal care at the zoo. "We were very optimistic about the future of this calf."
Zoo vets said the calf had congenital defects.
The zoo had announced in March that the elephant, also known as Rani, was pregnant again after already losing two calves.
Rani had her first calf, Keemaya, in 2004 and another, Malti, in 2007. The first died shortly after being rejected by its mother at birth.
The second was also rejected, but the two bonded a few months later. Malti died about a year later of elephant herpes virus.
Elephant to remain in breeding program
The Calgary Zoo says Rani will continue to be part of the breeding program.
Julie Woodyer with Zoocheck Canada said that's where the real heartbreak lies.
"I think it's selfish, absolutely selfish," she said. "Let's hope they change their mind on that. It's completely irresponsible to be breeding those elephants."
The zoo had already announced that it is looking for a new location for its elephant herd to provide a better atmosphere for reproduction.
The zoo had spent roughly $250,000 improving the facility in anticipation of Rani giving birth.
It’s anticipated the zoo’s lone bull, Spike, will be moved out first in co-operation with the Miami Zoo — which still owns him — and after consultation with the Asian Elephant Species Survival Plan.
The three female elephants — Kamala, Swarna and Maharani — will be kept together as a family unit when they are moved, the zoo said.
Woodyer says there are only two facilities in all of North America equipped to house Rani and her herd but that neither would allow breeding.
"Rani must be allowed to breed again — it's the right thing for her, it's the right thing for the breeding program," said Veasey.
"But also we don't necessarily want that to prevent us moving the herd on at the right time."
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