Jenny died Aug. 23 after a heart attack caused by complications from an aggressive form of cancer, the Belfast Telegraph reported.
"We were unaware of any ill-health -- like many of our animals, she was so good at hiding it," said the zoo manager, Mark Challis.
"Then, on Thursday last week, the cameras showed she had had a collapse in the paddock and she had a second heart attack early on Friday morning, which killed her," he said.
"Thankfully it was relatively quick and relatively painless. She was one of the zoo's most popular animals and we've had lots of Facebook messages about her."
Zoo curator Alyn Cairns said: "Jenny's death is a huge loss to the zoo's Asian elephant herd but she will also be greatly missed by the keepers who worked with her every day for the last four years. We are delighted that we were able to see her enjoy her last few years at the zoo."