A spokesperson confirmed to The Local on Wednesday that the zoo had closed after vets discovered skin lesions around the mouths and noses of the animals.
A statement on the park's website added that vets had taken samples from the lambs and goats and were currently waiting for test results. Staff suspect that the animals have contracted a skin disease similar to eczema that can be passed between animals and humans and vice versa.
Lars Kristensen, one of the vets working at the zoo told the TT news agency that humans symptoms would include "sores and blisters on hands".
"In consultation with veterinary staff it has been decided to shut the petting zoo for safety's sake," read the park's online post.
"This is so that the children should not have contact with the animals," it added.
It added that anyone who has visited the petting zoo and has experienced skin problems should seek medical advice.
Gothenburg's Slottskogen is a 137 hectare space that is home to Nordic animals including elks, deer, owls, Gotland ponies and Gute sheep as well as piglets, hairy goats, lambs, seals, ducks and penguins.
The petting zoo has only just reopened for its summer season after a winter break. It remains unclear when families will be able to return to the area.