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Significance: Machine learning models for the direct extraction of tissue parameters from hyperspectral images have been extensively researched recently, as they represent a faster alternative to the well-known iterative methods such as inverse Monte Carlo and inverse adding-doubling (IAD)., Aim: We aim to develop a Bayesian neural network model for robust prediction of physiological parameters from hyperspectral images., Approach: We propose a two-component system for extracting physiological parameters from hyperspectral images. First, our system models the relationship between the measured spectra and the tissue parameters as a distribution rather than a point estimate and is thus able to generate multiple possible solutions. Second, the proposed tissue parameters are then refined using the neural network that approximates the biological tissue model., Results: The proposed model was tested on simulated and in vivo data. It outperformed current models with an overall mean absolute error of 0.0141 and can be used as a faster alternative to the IAD algorithm., Conclusions: Results suggest that Bayesian neural networks coupled with the approximation of a biological tissue model can be used to reliably and accurately extract tissue properties from hyperspectral images on the fly., (© 2025 The Authors.)