Fruit ripeness prediction (FRP) is a classification-based agricultural computer vision task that has attracted much attention, thanks to its wide-ranging advantages in agriculture field for both pre-harvest and post-harvest management. Accurate and timely FRP can be achieved using machine/deep learning-based hyperspectral image classification techniques. However, challenges including the limited availability of labeled data and the lack of robust methods generalizable to various hyperspectral cameras and fruit types can compromise the effectiveness of hyperspectral image-based FRP. Addressing these challenges, this paper introduces Fruit-HSNet, a machine learning architecture specifically designed for hyperspectral classification of fruit ripeness. Fruit-HSNet incorporates a spatio-spectral feature extraction module based on Fourier Transform and central pixel spectral signature followed by learnable feature fusion and a classifier optimized for ripeness classification. The proposed architecture was evaluated using the DeepHS Fruit dataset, the largest publicly available labeled real-world hyperspectral dataset for predicting fruit ripeness, which includes five different types of fruits—avocado, kiwi, mango, kaki, and papaya—captured with three distinct hyperspectral cameras at various stages of ripeness. Experimental results highlight that Fruit-HSNet substantially outperforms existing deep learning methods, from baseline to state-of-the-art models, with improvements of 12%, achieving a new state-of-the-art overall accuracy of 70.73%.