The solution of the Poisson equation contributes a significant portion to the overall runtime in computational fluid dynamics (CFD) when solving the incompressible Navier-Stokes equations. Multigrid methods are utilized frequently to accelerate its solution, however, their performance highly depends on a series of solver settings. The optimal solver settings are subject to the encountered flow physics and generally unknown beforehand. Deep reinforcement learning (DRL) is able to efficiently find optimal control laws for complex optimization problems by interacting with an environment. The present thesis aims to implement a DRL training routine in order to learn optimal multigrid solver settings. The resulting policies are able to adjust and maintain the optimal solver settings during runtime, leading to a decrease in the required execution time by up to 22% compared to the default settings. The policies are able to outperform a priori unknown optimal solver settings by up to 3%, as a consequence of the runtime optimization. This thesis further provides insights into the choice of the optimal solver settings with respect to the encountered flow physics and domain decomposition of the simulation. The trained policies generalize to unseen environments to some degree provided the modeling of the flow as well as the numerical setup is similar. However, the overall generalization capabilities to environments that have not been part of the training are not optimal yet and remain a matter of future studies.