The zoo, which has been shut since 22 March, will not re-open before 4 April at the earliest.
It is currently blanketed in up to two feet of snow.
A statement said: "The continued closure is to ensure visitor safety and animal care."
Belfast Zoo said a number of mature trees have been damaged or have fallen as a result of the blizzard which battered Northern Ireland last week.
Access to some animal enclosures and pathways has been blocked.
Zoo manager Mark Challis said it has been a difficult time for keepers.
"Our keepers have been working against the elements to care for our animals," he said.
"As the majority of our animals have been born in Belfast or in other European zoos they are acclimatised to the cold weather.
"In fact some of our animals, such as the penguins, positively thrive in this environment."
Mr Challis explained that the closure is "disappointing", but added that every effort is being made to fix the damage so that normal service can be resumed.
"This is especially disappointing as we have been working hard towards our busy Easter season," he said.
"I can assure all of our visitors that the entire zoo team and contractors are working tirelessly to return the site to normal conditions."