Some situations require one to quickly stop an initiated response. Recent evidence suggests that rapid stopping engages a mechanism that has diffuse effects on the motor system. For example, stopping the hand dampens the excitability of the task-irrelevant leg. However, it is unclear whether this "global suppression" could apply across wider motor modalities. Here we tested whether stopping speech leads to suppression of the task-irrelevant hand. We used Transcranial Magnetic Stimulation over the primary motor cortex with concurrent electromyography from the hand. We found that when speech was successfully stopped the motor evoked potential from the task-irrelevant hand was significantly reduced compared to when the participant failed to stop speaking, or responded on non stop signal trials, or compared to baseline. This shows that when speech is quickly stopped, there is a broad suppression across the motor system. This has implications for the neural basis of speech control and stuttering. (Contains 1 table and 1 figure.)