The evaluation of cheese texture during the ripening phase usually involves invasive and destructive methods, as well as specialized equipment, which are non-advantageous characteristics for routine tests. Therefore, new noninvasive technologies for measuring texture properties are being studied. In this paper, forty Swiss-type cheese samples were prepared and carried to the ripening stage. During this process, hyperspectral images (HSI) were obtained in reflectance mode, in a range of 400–1000 nm. The hardness of Swiss-type cheese was measured using the technique of texture profile analysis. The relationship between spectral profiles and hardness values was modeled using two types of regression models, i.e., partial least squares regression (PLSR) and artificial neural networks (ANN). For both PLSR and ANN, two models were created, the first one uses all the wavelengths and the second makes a selection of the relevant wavelengths. The ANN models showed slightly better performance than the PLSR models. As result, it is possible to use the proposed technique (HSI + ANN) to predict the texture properties of Swiss-type cheeses throughout the ripening period.