Mirror movements (MM) refer to involuntary contractions occurring in homologous muscles contralateral to the voluntary movements. In right-handers, greater MM occur in the right hand during movements of the non-dominant left hand than conversely. However, it remains to know if such behavioural asymmetry of MM relies only on motor processes or if it is also related to attentional and executive processes. This study explores MM behavioural asymmetry and its cerebral correlates with electroencephalography in 14 right-handed healthy adults. We investigated the quantity and the intensity of MM and the associated task-related power changes in the beta band over central regions (motor processes), in the alpha band over the parietal regions (attentional processes) and in the theta band over frontal regions (executive processes). Behavioural results revealed greater MM in the right hand when the left hand was active than the reverse. This behavioural asymmetry was associated with asymmetry in the cortical activations over motor areas. Greater MM in the right hand correlated with activation over the contralateral left motor region, revealing that selective inhibition of one hand induced activation of the motor cortex leading to MM. In addition, increased cortical activations over parietal and fronto-mesial regions suggest that an increase of attentional and executive processes is required to inhibit one hand, independently of its side. All in all, this study highlights that side-specific motor and non-side-specific attentional and executive processes are associated to the MM asymmetry.