Fundamental movement patterns require continuous skeletal muscle coordination, where muscle fibers with different timing of activation synchronize their dynamics across muscles with distinct functions. It is unknown how muscle fibers integrate as a network to generate and fine tune movements. We investigate how distinct muscle fiber types synchronize across arm and chest muscles, and respond to fatigue during maximal push-up exercise. We uncover that a complex inter-muscular network of muscle fiber cross-frequency interactions underlies push-up movements. The network exhibits hierarchical organization (sub-networks/modules) with specific links strength stratification profile, reflecting distinct functions of muscles involved in push-up movements. We find network reorganization with fatigue where network modules follow distinct phase-space trajectories reflecting their functional role and adaptation to fatigue. Consistent with earlier observations for squat movements under same protocol, our findings point to general principles of inter-muscular coordination for fundamental movements, and open a new area of research, Network Physiology of Exercise.