Alliance North Belfast Councillor Nuala McAllister said she had contacted Belfast City Council, which runs the zoo, about a review into the containment of animals, with a particular focus on safety measures.
Chimpanzees used branches felled by a storm to escape from their zoo enclosure, in front of witnesses, who filmed the whole episode.
Visitors described seeing one of the escapees emerge from the bushes onto a path while others were sitting on top of their enclosure wall.
Shocked families recorded the moment the great ape pulled itself up the wall and began to roam free along the pathways in Belfast Zoo.
Belfast City Council, which runs the zoo, said the chimpanzee was only out of the pen for a brief amount of time.
Ms Monaghan later told BBC she was "petrified" at seeing the chimps escape.
Belfast Zoo said Saturday's incident was "highly unusual".
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But the mother of two said the animal was "not aggressive" and "just watched".
She added that it was "easy to think it was funny" after the encounter, but that the experience was still "quite unsafe".
Only one chimp appears to have fully left the enclosure, while others simply sat on their enclosure wall.
"Zookeepers were present as the chimpanzee quickly returned from an adjacent wall to the rest of the group inside the enclosure", a spokeswoman said.
The zoo's Alyn Cairns said the zoo's chimps were "quite cowardly" so went back into their enclosure themselves during the incident, which happened as the zoo was closing up for the day.
He said zoo officials will now "review" the situation, but they don't want to remove the trees.
Mr Cairns added that the enclosure now trees to make it feel more natural for the chimps.
He added that once they were safely contained, the chimps were locked into an inner enclosure.