Hyperspectral optoacoustic microscopy (OAM) enables obtaining images with label-free biomolecular contrast, offering excellent perspectives as a diagnostic tool to assess freshly excised and unprocessed tissues. However, time-consuming raster-scanning image formation currently limits the translation potential of OAM into the clinical setting-for instance, in intraoperative histopathological assessments-where micrographs of excised tissue need to be taken within a few minutes for fast clinical decision-making. Here, we present a non-data-driven computational framework tailored to enable fast OAM by sparse data acquisition and model-based image reconstruction, termed Bayesian raster-computed optoacoustic microscopy (BayROM). Unlike conventional machine learning, BayROM doesn't require training datasets, but instead, it employs 1) optomechanical system properties to define a forward model and 2) prior knowledge of the imaged samples to facilitate reconstructing images based on the sparsely acquired data. We show that BayROM enables acquiring micrographs ten times faster and with structural similarity (SSIM) indices greater than 0.93 compared to conventional raster scanning microscopy, thus facilitating the clinical translation of OAM for fast, label-free intraoperative histopathology.