The sensory input arising from our own movements is predictable to varying degrees. This predictability plays a role in action selection, initiation, and the evaluation of action outcomes, and should therefore influence neural processing both before and after movement. Here, we examined the effect of sensory predictability on pre- and post-movement processing, as reflected in two signals in the human electroencephalogram (EEG): the Readiness Potential (RP) and the post-movement beta rebound (PMBR). Thirty-six participants performed self-paced button presses in three conditions, in which they received either highly predictable auditory feedback (always the same sound), weakly predictable auditory feedback (an unpredictable, pseudo-random sound), or no auditory feedback. In the former two conditions, 20% of button presses unexpectedly elicited no sound. In these omission trials, we observed brain responses, which indicated that participants formed sensory predictions of a varying level of detail. Crucially, RP amplitude was increased when button presses always produced the same sound, compared to pseudo-random sounds, or no sound, with the latter two conditions showing no difference. In contrast, the PMBR was unchanged across conditions. Our results indicate that the specificity of sensory prediction influences the pre-movement processes reflected in the RP, even when these details are not task-relevant.