Background: EEG mu-desynchronization is an index of motor resonance (MR) and is used to study social interaction deficiencies, but finding differences in mu-desynchronization does not reveal how nonlinear brain dynamics are affected during MR. The current study explores how nonlinear brain dynamics change during MR. We hypothesized that the complexity of the mu frequency band (8–13 Hz) changes during MR, and that this change would be frequency specific. Additionally, we sought to determine whether complexity at baseline and changes in complexity during action observation would predict MR and changes in network dynamics.Methods: EEG was recorded from healthy participants (n = 45) during rest and during an action observation task. Baseline brain activity was measured followed by participants observing videos of hands squeezing stress balls. We used multiscale entropy (MSE) to quantify the complexity of the mu rhythm during MR. We then performed post-hoc graph theory analysis to explore whether nonlinear dynamics during MR affect brain network topology.Results: We found significant mu-desynchronization during the action observation task and that mu entropy was significantly increased during the task compared to rest, while gamma, beta, theta, and delta bands showed decreased entropy. Moreover, resting-state entropy was significantly predictive of the degree of mu desynchronization. We also observed a decrease in the clustering coefficient in the mu band only and a significant decrease in global alpha efficiency during action observation. MSE during action observation was strongly correlated with alpha network efficiency.Conclusions: The current findings suggest that the desynchronization of the mu wave during MR results in a local increase of mu entropy in sensorimotor areas, potentially reflecting a release from alpha inhibition. This release from inhibition may be mediated by the baseline MSE in the mu band. The dynamical complexity and network analysis of EEG may provide a useful addition for future studies of MR by incorporating measures of nonlinearity.