It may have gotten it stuck under something in the habitat. Their bones are so fragile as it is, and the little Peepers are so tiny. Just like us, they can get injured just doing their normal thing.
I would also recommend amputation. Even if the broken bone could heal together, the chance of infection is too high to risk it. If it heals up well, it should be okay. You may need to watch it to make sure it gets enough food, but otherwise would be fine. I've found a couple of frogs that unfortunately wandered into the home and were discovered by the cats. I've seen them recover fairly well from this kind of trauma. They're tough little critters!