Hand motor function is often severely affected in stroke patients. Non-satisfying recovery limits reintegration into normal daily life. Understanding stroke-related network changes and identifying common principles that might underlie recovered motor function is a prerequisite for the development of interventional therapies to support recovery. Here, we combine the evaluation of functional activity (multichannel electroencephalography) and structural integrity (diffusion tensor imaging) in order to explain the degree of residual motor function in chronic stroke patients. By recording neural activity during a reaching and grasping task that mimics activities of daily living, the study focuses on deficit-related neural activation patterns. The study showed that the functional role of movement-related beta desynchronization in the supplementary motor area (SMA) for residual hand motor function in stroke patients depends on the microstructural integrity of the corticospinal tract (CST). In particular, in patients with damaged CST, stronger task-related activity in the SMA was associated with worse residual motor function. Neither CST damage nor functional brain activity alone sufficiently explained residual hand motor function. The findings suggest a central role of the SMA in the motor network during reaching and grasping in stroke patients, the degree of functional relevance of the SMA is depending on CST integrity.