We provide a theoretical framework for model predictive control of infinite-dimensional systems, like, e.g., nonlinear parabolic PDEs, including stochastic disturbances of the input signal, the output measurements, as well as initial states. The necessary theory for implementing the MPC step based on an LQG design for infinite-dimensional linear time-invariant systems is presented. We also briefly discuss the necessary ingredients for the numerical computations using the derived theory.