Fiona, an adult Gentoo penguin, died in December, about eight days after she had surgery to remove the 25-centimetre stick.
Zoo curator Jamie Dorgan says the penguin seemed to be recovering well from surgery, but eight days after the operation, they found it dead in a holding room where it was being kept during recovery.
He says penguins are curious and may have thought the stick was nesting material.
Dorgan says staff do check the exhibit before letting out the birds and that day was no exception.
He called it "flukey", adding the zoo didn't put out a news release at the time because officials don't consider the death to be anything out of the ordinary.
"We don't put out a press release for every animal death. We are a large zoo, we have a lot of animals, all kinds of comings and goings, births, deaths, acquisitions...
"We've been incredibly lucky to get through a full year with 46 birds and this is the first death we had. Penguins have an average life span of somewhere around 20 years; realistically, we should be over the years seeing an average of two penguins dying a year as we go along. Statistically that's the way it is."
The zoo's penguin exhibit opened in February 2012.
The zoo has experienced several animal deaths in recent years including a hippo, wild goat, capybara and stingrays.
In December, two employees were disciplined after a great grey owl died.
It happened while the workers were transferring it from one holding area to another and the bird flew into a gate.
The zoo said an investigation showed the workers did not take reasonable precautions to ensure the owl's safety.
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