"We pride ourselves on our conservation and breeding programme of cotton top Tamarin monkeys," said the theme park's managing director Colin Bryan.
"We are extremely concerned and distressed at the theft. The monkeys have a careful daily routine and we employ experts who look after them. We need the public's help and information to get them back safely."
Tamarin monkeys are native to the Colombian rainforests in South America. They have long tongues which they use to extract sap from trees and catch frogs.
Tommy and Tina have been at the theme park - which is also home to marmosets and chimpanzees - for about 15 years, while baby Terry was born in captivity about six years ago.
The primates, who have a high metabolism, are fed with special vitamin cakes and jelly each morning and fruit and vegetables in the afternoon.
Each is micro-chipped either under the shoulder or rump and should be easily identifiable if the thieves attempt to sell them on.
"It is not clear why these have been stolen, but it was determined theft," said Trevor Steventon from Staffordshire police, whose detectives were on the case.