In vision, the discovery of the phenomenon of saccadic suppression of displacement has made important contributions to the understanding of the stable world problem. Here, we report a similar phenomenon in the tactile modality. When scanning a single Braille dot with two fingers of the same hand, participants were asked to decide whether the dot was stationary or whether it was displaced from one location to another. The stimulus was produced by refreshable Braille devices that have dots that can be swiftly raised and recessed. In some conditions, the dot was stationary. In others, a displacement was created by monitoring the participant’s finger position and by switching the dot activation when it was not touched by either finger. The dot displacement was of either 2.5 mm or 5 mm. We found that in certain cases, displaced dots were felt to be stationary. If the displacement was orthogonal to the finger movements, tactile suppression occurred effectively when it was of 2.5 mm, but when the displacement was of 5 mm, the participants easily detected it. If the displacement was medial–lateral, the suppression effect occurred as well, but less often when the apparent movement of the dot opposed the movement of the finger. In such cases, the stimulus appeared sooner than when the brain could predict it from finger movement, supporting a predictive rather than a postdictive differential processing hypothesis.