Increasing evidence suggests that the natural world has a special status for our sensory and cognitive functioning. The mammalian sensory system is hypothesized to have evolved to encode natural signals in an efficient manner. Exposure to natural stimuli, but not to artificial ones, improves learning and cognitive function. Scale-invariance, the property of exhibiting the same statistical structure at different spatial or temporal scales, is common to naturally occurring sounds. We recently developed a 3-parameter model to capture the essential characteristics of water sounds, and from this generated both scale-invariant and variable-scale sounds. In a previous study, we found that adults perceived a wide range of the artificial scale-invariant, but not the variable-scale, sounds as instances of natural sounds. Here, we explored the ontogenetic origins of these effects by investigating how young infants perceive and categorize scale-invariant acoustic stimuli. Even though they have several months of experience with natural water sounds, infants aged 5 months did not show a preference, in the first experiment, for the instances of the scale-invariant sounds rated as typical water-like sounds by adults over non-prototypical, but still scale-invariant instances. Scale-invariance might thus be a more relevant factor for the perception of natural signals than simple familiarity. In a second experiment, we thus directly compared infants' perception of scale-invariant and variable-scale sounds. When habituated to scale-invariant sounds, infants looked significantly longer to a change in sound category from scale-invariant to variable-scale sounds, whereas infants habituated to variable-scale sounds showed no such difference. These results suggest that infants were able to form a perceptual category of the scale-invariant, but not variable-scale sounds. These findings advance the efficient coding hypothesis, and suggest that the advantage for perceiving and learning about the natural world is evident from the first months of life.