Recent studies have made great progress in functional brain network analysis by modeling the brain as a network of Regions of Interest (ROIs) and leveraging their connections to understand brain functionality and classify brain disorders. Various deep learning architectures, including Convolutional Neural Networks, Graph Neural Networks, and the recent Transformer, have been developed. However, despite the increasing complexity of these models, the performance gain has not been as salient. Furthermore, the escalating model complexity will exacerbate the gap between theoretical research and real-world deployment. To mitigate this gap, we revisit the simplest deep learning architecture, the Multi-Layer Perceptron (MLP), and propose a pure MLP-based method, named BrainNetMLP for functional brain network classification. Specifically, BrainNetMLP incorporates a dual-branch structure to jointly capture spatial connectivity and temporal dynamics in spectral domain, enabling spatiotemporal feature fusion for precise classification. Besides, considering the fully-connected property of MLPs, we also propose an Edge-Degree Guided Pruning technique to remove redundant parameters of MLPs, further improving the efficiency. We evaluate our proposed BrainNetMLP on two public and popular brain network classification datasets, the Human Connectome Project (HCP) and the Autism Brain Imaging Data Exchange (ABIDE). Experimental results demonstrate pure MLP-based methods can achieve state-of-the-art accuracy and efficiency, revealing the potential of MLP-based models as more efficient yet effective alternatives in functional brain network classification. The code is available at https://github.com/JayceonHo/BrainNetMLP