A physics-driven generative adversarial network (GAN) was established here for single-pixel hyperspectral imaging (HSI) in the infrared spectrum, to eliminate the extensive data training work required by traditional data-driven model. Within the GAN framework, the physical process of single-pixel imaging (SPI) was integrated into the generator, and the actual and estimated one-dimensional (1D) bucket signals were employed as constraints in the objective function to update the network's parameters and optimize the generator with the assistance of the discriminator. In comparison to single-pixel infrared HSI methods based on compressed sensing and physics-driven convolution neural networks, our physics-driven GAN-based single-pixel infrared HSI can achieve higher imaging performance but with fewer measurements. We believe that this physics-driven GAN will promote practical applications of computational imaging, especially various SPI-based techniques.