Artificial intelligence (AI) has made significant strides towards efficient online processing of sensory signals at the edge through the use of deep neural networks with ever-expanding size. However, this trend has brought with it escalating computational costs and energy consumption, which have become major obstacles to the deployment and further upscaling of these models. In this Perspective, we present a neuro-inspired vision to boost the energy efficiency of AI for perception by leveraging brain-like dynamic sparsity. We categorize various forms of dynamic sparsity rooted in data redundancy and discuss potential strategies to enhance and exploit it through algorithm-hardware co-design. Additionally, we explore the technological, architectural, and algorithmic challenges that need to be addressed to fully unlock the potential of dynamic-sparsity-aware neuro-inspired AI for energy-efficient perception.