Visitors to the Port Lympne Reserve, near Hythe in Kent, were moved to safety when the two-year-old, called Kitwana, got out on Sunday.
Animal director Adrian Harland said the cheetah was "calm and pacing the enclosure fence, looking to get back in" and there was "no real threat".
He was enticed back into the enclosure with food after almost 30 minutes.
Mr Harland said the intervention of a vet was not required.
He added: "He climbed out to get back with his mother, after he was separated to stop him eating all her dinner.
"We have secured the enclosure's perimeter fencing to ensure the cheetah cannot climb out again."
A cheetah escaped from its enclosure at a wild animal park while the attraction was open to the public.