The pure Rothschild female was born on January 27 and was the height of a full-grown man.
Operations manager Paul Whitehorn said the birth took just 20 minutes.
“[She] started life off dropping from about six-foot above the ground … so it’s equivalent to a giraffe slap on the bottom. It’s a bit of a splat,” he said.
“Mum gave her a bit of a clean-up then literally about half an hour later she’s trying to jump up on her feet, and by the end of the day she was running around like a lunatic. She’s amazing.”
Zoo owner Sally Padey said the delivery of the 1.5 metre animal was a “touching moment”.
“I am still amazed and relieved when I see that little baby giraffe with its long spindly legs shaking, and its coat still wet, get to its feet and start nursing,” she said.
The baby is the fifth born to mother Shani in six years and is yet to be named.
The species, which inhabits Kenya and northern Uganda, is threatened by drought, hunting, poaching and habitat encroachment.