Reach movements are characterized by multiple kinematic variables that can change with age or due to medical conditions such as movement disorders. While the neural control of reach direction is well investigated, the elements of the neural network regulating speed (the nondirectional component of velocity) remain uncertain. Here, we used a custom made magnetic resonance (MR)‐compatible arm movement tracking system to capture the real kinematics of the arm movements while measuring brain activation with functional magnetic resonance imaging to reveal areas in the human brain in which BOLD‐activation covaries with the speed of arm movements. We found significant activation in multiple cortical and subcortical brain regions positively correlated with endpoint (wrist) speed (speed‐related activation), including contralateral premotor cortex (PMC), supplementary motor area (SMA), thalamus (putative VL/VA nuclei), and bilateral putamen. The hand and arm regions of primary sensorimotor cortex (SMC) and a posterior region of thalamus were significantly activated by reach movements but showed a more binary response characteristics (movement present or absent) than with continuously varying speed. Moreover, a subregion of contralateral SMA also showed binary movement activation but no speed‐related BOLD‐activation. Effect size analysis revealed bilateral putamen as the most speed‐specific region among the speed‐related clusters whereas primary SMC showed the strongest specificity for movement versus non‐movement discrimination, independent of speed variations. The results reveal a network of multiple cortical and subcortical brain regions that are involved in speed regulation among which putamen, anterior thalamus, and PMC show highest specificity to speed, suggesting a basal‐ganglia‐thalamo‐cortical loop for speed regulation.