High-precision edge detection plays a crucial role in surface defect identification and quality control in industrial manufacturing; however, conventional imaging methods still suffer from limited capability in resolving microscale defects due to constraints in spatial resolution and signal-to-noise ratio. In this work, we propose a physics-prior-driven generative adversarial network–based near-infrared Fourier single-pixel hyperspectral edge imaging method. By loading measurement bases with differential-operator structures onto a spatial light modulator, the spatial response of the Laplacian of Gaussian operator is embedded into the single-pixel modulation and detection process. This design enhances the sensitivity of singlepixel measurements to higher-order spatial intensity variations, enabling direct amplification of edge-related high spatial frequency information at the data acquisition stage. On the reconstruction side, a generative adversarial network incorporating the single-pixel integral measurement model is developed, with physical consistency and spectral correlation constraints imposed during optimization. This framework enables the recovery of high-resolution two-dimensional edge images from bucket signals across 512 near-infrared spectral channels. Experimental results demonstrate that, under sparse sampling conditions, the proposed method significantly improves edge resolution and spectral fidelity compared with conventional reconstruction strategies, allowing reliable identification of microscale surface scratches that are diffcult to resolve using traditional approaches. This work provides a new physics–data collaborative imaging paradigm for hyperspectral single-pixel imaging in applications such as material characterization, surface defect inspection, and precision metrology.