DSC-MRI perfusion is a medical imaging technique for diagnosing and prognosing brain tumors and strokes. Its analysis relies on mathematical deconvolution, but noise or motion artifacts in a clinical environment can disrupt this process, leading to incorrect estimate of perfusion parameters. Although deep learning approaches have shown promising results, their calibration typically rely on third-party deconvolution algorithms to generate reference outputs and are bound to reproduce their limitations. To adress this problem, we propose a physics-informed autoencoder that leverages an analytical model to decode the perfusion parameters and guide the learning of the encoding network. This autoencoder is trained in a self-supervised fashion without any third-party software and its performance is evaluated on a database with glioma patients. Our method shows reliable results for glioma grading in accordance with other well-known deconvolution algorithms despite a lower computation time. It also achieved competitive performance even in the presence of high noise which is critical in a medical environment.