Humans are able to judge the speed of an object's motion by touch. Research has suggested that tactile judgment of speed is influenced by physical properties of the moving object, though the neural mechanisms underlying this process remain poorly understood. In the present study, functional magnetic resonance imaging was used to investigate brain networks that may be involved in tactile speed classification and how such networks may be affected by an object's texture. Participants were asked to classify the speed of 2-D raised dot patterns passing under their right middle finger. Activity in the parietal operculum, insula, and inferior and superior frontal gyri was positively related to the motion speed of dot patterns. Activity in the postcentral gyrus and superior parietal lobule was sensitive to dot periodicity. Psycho-physiological interaction (PPI) analysis revealed that dot periodicity modulated functional connectivity between the parietal operculum (related to speed) and postcentral gyrus (related to dot periodicity). These results suggest that texture-sensitive activity in the primary somatosensory cortex and superior parietal lobule influences brain networks associated with tactually-extracted motion speed. Such effects may be related to the influence of surface texture on tactile speed judgment.