The animals were caught on video climbing over the wall and walking calmly around the attraction in Northern Ireland on Saturday.
One adult chimpanzee passed just feet from four children enjoying a family trip to the zoo.
Manager Alyn Cairns said the chimpanzees soon returned to the enclosure of their own accord.
“They’re intelligent primates and know they’re not supposed to be out of their enclosure, so got back in themselves,” Mr Cairns told the BBC.
“We think what has happened is that the trees in their enclosure have been weakened by the storms and so they’ve been able to break them and use them as a ladder to get out.
“We like things to be natural in their enclosure, to have trees in it, but we will review it.”
Footage of the roaming chimpanzees was posted on Twitter by Elaine Monaghan, whose grandchildren were at the zoo at the time of the escape.
She said: “Why weren’t the enclosures checked? This could have ended very badly. This is how close it came to my grandchildren.”
Responding to comments from other users, Ms Monaghan said that the children were “buzzing” after the incident and that her daughter was “a lot calmer than I’d have been”.
“Just happy it ended well,” she added. “Having four children with them they tried to act as calmly as possible so as not to frighten the kids. Everyone has their own way of reacting. Had it been me I’d have run for the hills.”
It came just a month after an endangered red panda named Amber managed to escape from the same zoo.
Police launched a public appeal to trace the Himalayan cub and she was eventually found in a residential garden in Collinbridge, Newtonabbey.
Belfast Zoo has seven chimpanzees and, according to its website, its dominant male is named Andy.
A Belfast City Council spokesperson said in a statement that one chimpanzee “briefly” left its enclosure.
“Zookeepers were present as the chimpanzee quickly returned from an adjacent wall to the rest of the group inside the enclosure,” a spokeswoman said.
“Belfast Zoo would like to thank members of the public who helped raise the alarm as zookeepers moved in to return the animal to its enclosure.”
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