The soft play centre, which opened in June last year, recently created an exotic pets area that was home to meerkats, snakes, tortoises, iguanas, owls and genets, according to posts on social media.
East Hertfordshire Council said it was aware that animals were on the site.
It said it wrote to the company at the beginning of the month “to inform them of the need to apply for a licence”.
It said it had “not received a response from them”.
The fire service said: “While carrying out the fire investigation, we incredibly discovered a baby tortoise alive in the aftermath, despite earlier fears that all the animals had died.
“A small but powerful moment after a very difficult incident.”