Positive-frequency Wightman function and vacuum expectation values of the energy–momentum tensor are computed for a massive scalar field with general curvature coupling parameter, satisfying the Robin boundary condition on a uniformly accelerated infinite plate. Both the regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are investigated. For the case (ii) the electromagnetic field is considered as well. The mode summation method is used in combination with a variant of the generalized Abel–Plana formula. This allows us to present the expectation values in the form of a sum of the purely Rindler and boundary parts. Near the plate surface, the vacuum energy–momentum tensor is dominated by the boundary term. At large distances from the plate and near the Rindler horizon, the main contribution comes from the purely Rindler part. In the RL region, the vacuum energy density of the electromagnetic field is negative near the horizon and is positive near the plate.