The cub is the first polar bear to be born in the UK in 25 years.
Staff have not yet seen the new cub and say there is the possibility that more than one cub has been born.
The mother bear, Victoria, is one of three adult polar bears at the Highland Wildlife Park at Kincraig, near Aviemore.
RZSS said “high-pitched noises” made by the cub could be heard from Victoria’s maternity den just before Christmas.
The last polar bear cubs born in the UK were twins at Flamingo Land in Yorkshire on 8 December 1992.
Una Richardson, the park’s head keeper responsible for carnivores, said: “We first heard promising noises in the week before Christmas and these have now continued into the new year.
“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.
Victoria was brought to the Highland Wildlife Park, which also has two male bears, last year.
Ms Richardson added: “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.
“We will continue to monitor Victoria and very much hope for the best possible news when she emerges around March.
“Until then, Victoria’s enclosure will be closed to the public and keeper activity will be at a minimum to give her offspring every chance of survival.”
Arktos, the male bear Victoria mated with, is one of the park’s other adult bears. He was brought from Hanover Zoo in Germany and is in a separate enclosure from the female bear.