The prevalence of AI-generated imagery has raised concerns about the authenticity of astronomical images, especially with advanced text-to-image models like Stable Diffusion producing highly realistic synthetic samples. Existing detection methods, primarily based on convolutional neural networks (CNNs) or spectral analysis, have limitations when used independently. We present AstroSpy, a hybrid model that integrates both spectral and image features to distinguish real from synthetic astronomical images. Trained on a unique dataset of real NASA images and AI-generated fakes (approximately 18k samples), AstroSpy utilizes a dual-pathway architecture to fuse spatial and spectral information. This approach enables AstroSpy to achieve superior performance in identifying authentic astronomical images. Extensive evaluations demonstrate AstroSpy's effectiveness and robustness, significantly outperforming baseline models in both in-domain and cross-domain tasks, highlighting its potential to combat misinformation in astronomy.