A dynamic observer is presented which can reconstruct the internal state of a tokamak fusion plasma, consisting of the spatial distribution of current and temperature, from measurements. Today, the internal plasma state is usually reconstructed by solving an ill-conditioned inversion problem using a large number of measurements at one point in time. Such an approach does not take into account the time evolution of the underlying dynamical system (the plasma) and strongly relies on (technically challenging) internal measurements. The observer-based approach presented here includes the dynamics of the plasma current and temperature, modeled by a set of coupled nonlinear 1-D PDEs which are discretized in space and time to yield a finite-dimensional nonlinear model. The observer, which is based on an Extended Kalman Filter, estimates the state of an augmented model which includes additive state disturbances modeled as a random walk. Simulation results demonstrate the effectiveness of this observer in the case of perturbed models and input disturbances.