We consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casimir potential energy between the cavity walls. We also find a change of the field energy density in the cavity, particularly relevant in the proximity of the mobile wall, yielding a correction to the Casimir-Polder interaction with a polarizable body placed inside the cavity. Similarities and differences of our results with the dynamical Casimir effect are also discussed.