That is extremely dangerous. From what I understand, falls from even a small height can cause internal damage. Immortalia said "Even a fall off of something a few inches high can cause enough damage to kill a hedgie. Whether it be broken bones, or worse...Internal damage. Our hedgies aren't like the ones in the wild. While they can climb, they sometimes lack the quick response to ball up while falling. When I'm sitting on the ground, my hedgie climbs up into my lap and slides off in a superman pose, it doesn't occur to him to ball up."
You need to fix the cage immediately. One of the tricks to prevent climbing (quoted from hedgielover, who paraphrased Nancy)
"Basically you weave thick plastic, like place mats or report covers through the bars and the hedgehog will not be able to climb. I believe they have to be about 10" or 12" up."
Another option (again stolen from hedgielover) is:
"Most likely what would be easier than weaving the placemats would be to hole punch them and attach them with cable ties all along the bottom. You should attach the placemat at the top and bottom and attach them with at least three cable ties each for top and bottom ( one for each side and one for the middle)"
(I hope nobody minds me quoting them :? )