Accurate and efficient molecular property prediction is pivotal for drug discovery and safety assessment, yet it remains challenging due to the need to model complex chemical structures and shared substructure patterns across molecules. While Graph Neural Networks (GNNs) have become widely used to capture intra-molecular interactions, they fall short in modeling inter-molecular relationships and often fail to exploit chemical information from molecular fragmentation. In this work, we introduce FMol-HyG, a Fragmentation-based Molecular Hypergraph Attention Network, to overcome these limitations. We construct a unified molecular hypergraph where nodes represent molecular fragments and hyperedges represent molecules, allowing our model to encode higher-order associations. A dual attention mechanism then derives comprehensive molecular embeddings. Extensive experiments on six MoleculeNet classification benchmarks show that FMol-HyGachieves competitive performance against state-of-the-art models with significantly improved computational efficiency, underscoring the effectiveness of a unified, fragment-based hypergraph approach.