Our understanding of the adaptive processes that shape sensorimotor behaviour is largely derived from studying isolated movements. Studies of visuomotor adaptation, in which participants adapt cursor movements to rotations of the cursor's screen position, have led to prominent theories of motor control. In response to changes in visual feedback of movements, explicit (cognitive) and implicit (automatic) learning processes adapt movements to counter errors. However, movements rarely occur in isolation. The extent to which explicit and implicit processes drive sensorimotor adaptation when multiple movements occur simultaneously, as in the real world, remains unclear. Here, we address this problem in the context of speech and hand movements. Participants spoke in-time with rapid, hand-driven cursor movements. Using realtime auditory alterations of speech feedback, and visual rotations of the cursor's screen position, we induced sensorimotor adaptation in one or both movements simultaneously. Across three experiments (n = 184), we demonstrate that visuomotor adaptation is markedly impaired by simultaneous speech adaptation, and the impairment is specific to the explicit learning process. In contrast, visuomotor adaptation had no impact on speech adaptation. The results demonstrate that the explicit learning process in visuomotor adaptation is sensitive to movements in other motor domains. They suggest that speech adaptation may lack an explicit learning process.