The state estimation problem is considered for a diffusion-reaction system with spatially varying parameters defined on a 3-dimensional rectangular domain with the measured output being restricted to a single surface. For this, a backstepping-based observer design is applied, which enables to obtain the observer gains such that the observer error dynamics decays exponentially in the L2-norm. At first, an idealized system output restricted to a single surface is assumed as an available measurement. Secondly, in view of a practical realization of the proposed observer, the idealized system output is reconstructed from a set of finite-dimensional measurements. The observer error convergence and the applicability of the proposed approach are evaluated by means of numerical simulations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)