The decision to demolish the 1960s building comes after it was closed to the public earlier this month because it was found to meet less than 15% of the new-building standard for earthquake strength.
It previously operated seven days a week and attracted about 20,000 visitors a year.
The aquarium building, which houses 100 different types of fish, is the smallest of the three main buildings within the Portobello Marine Laboratory complex, with the other two remaining open.
The much larger 1980s-built marine laboratory building next to the aquarium and the newer New Zealand Marine Studies Centre on the landward side of the complex, will remain open.
Otago University property services director Barry MacKay said the aquarium building would be demolished in the "near future" and "initial planning" had begun for a new facility.
He said it was "too early" to say how much replacing the aquarium would cost and what the options for a new facility were.
Head of marine science Prof Gary Wilson said the university was "committed" to building a new aquarium accessible to the public, but was yet to decide where it would be built.
One of the options was to rebuild at the current site at Portobello, but he did not rule out building closer to the city.
"We haven't restricted our discussions to any particular sites at all," Prof Wilson said.
Among the considerations which would influence the final decision was ease of access for the public and the fact that moving away from Portobello would mean a new sea-water system would have to be built.
He said it was likely the new facility would first be opened for teaching programmes at the start of next year and then be opened to the public later in the year.
He added it was "not really" sad to see the old building go as it presented an opportunity to build a better facility.
"It's unfortunate that this has happened, but we have to make the best of it."
He did not know exactly when the building would be demolished, but said they would need new tanks for the animals before any work started.
Staff would not be affected by the decision to demolish the aquarium as none had been housed in the building since it was closed to the public.
