On their boy’s injuries, they added: “This will only be identified after casts and bandages are able to be removed and he can begin his rehabilitation journey.
“His rehabilitation journey is uncertain but we do know that it won’t be a short process.”
They revealed they also had a newborn baby to care for, adding : “We are extremely grateful for everyone’s generosity.
“We could never thank you enough for the support you have given our family in this horrible time.
“We have been living at the hospital for two weeks now and our son has undergone five surgeries.”
They said their boy would have to undergo at least two more surgeries.
The boy, who is from Cambridgeshire, was visiting the zoo with his family and was seriously injured “while in the enclosure”, Cambridgeshire Police previously said.
Chris Newman, the director of the National Centre for Reptile Welfare, previously told the that three members of the Johnson family had entered the enclosure.
On Friday, the owners of the zoo praised the “incredible speed and determination” of those who helped him.
On Wednesday, the boy’s family said they wished to “thank the staff at the zoo who rescued our son from the enclosure”.
The zoo has more than 100 animals, including lions, tigers and meerkats.
Crocodilians first arrived on the farm in 2006 and species now include broad snouted caiman, Nile crocodiles and American alligator.