Glioblastoma is an aggressive brain tumor that proliferates and infiltrates into the surrounding normal brain tissue. The growth of Glioblastoma is commonly modeled mathematically by diffusion-reaction type partial differential equations (PDEs). These models can be used to predict tumor progression and guide treatment decisions for individual patients. However, this requires parameters and brain anatomies that are patient specific. Inferring patient specific biophysical parameters from medical scans is a very challenging inverse modeling problem because of the lack of temporal data, the complexity of the brain geometry and the need to perform the inference rapidly in order to limit the time between imaging and diagnosis. Physics-informed neural networks (PINNs) have emerged as a new method to solve PDE parameter inference problems efficiently. PINNs embed both the data the PDE into the loss function of the neural networks by automatic differentiation, thus seamlessly integrating the data and the PDE. In this work, we use PINNs to solve the diffusion-reaction PDE model of glioblastoma and infer biophysical parameters from patient data. The complex brain geometry is handled by the diffuse domain method. We demonstrate the efficiency, accuracy and robustness of our approach.