The Royal Zoological Society of Scotland (RZSS) says its resident female polar bear, Victoria, gave birth at the Highland Wildlife Park.
They described the birth as an "outstanding achievement which will have interest across the world".
Staff at the park in Kincraig near Kingussie had heard "high-pitched sounds" from Victoria's maternity den.
Una Richardson, the head keeper responsible for carnivores, said: "Because we don't have sight inside her cubbing box we can't be sure if Victoria has had more than one cub but we can confirm the birth."
The wildlife park stressed, however, that the first three months are perilous for polar bear cubs, whether born in the wild or in captivity.
"While we are absolutely thrilled, we are not celebrating prematurely as polar bear cubs have a high mortality rate in the first weeks of life due to their undeveloped immune system and the mother's exaggerated need for privacy, with any disturbance risking the cub being killed or abandoned," Ms Richardson said.
The cub is currently being monitored and the mother's den will remain closed to the public with minimal keeper activity to give her offspring "every chance of survival".
Newborn polar bears are around 30cm long and weigh about the same as a guinea pig.
They are born blind and open their eyes when they are a month old.
Barbara Smith, the park's chief executive, said: "At RZSS we believe we have a duty to help protect this magnificent species, with the reduction in sea ice, the polar bear's primary seal hunting platform, predicted to significantly reduce numbers over the next 40 years.
"Our polar bears are part of the European Endangered Species Programme and we hope Victoria's offspring will survive to reinforce the captive population, which may be needed in the future to augment and help restore a markedly reduced and fragmented wild population."
The polar bear breeding season began in March last year, when Victoria mated with Arktos, one of the park's two males.
