(1) Background: Severe COVID-19 frequently leads to intensive care unit-acquired weakness (ICU-AW), a complex neuromuscular syndrome that may result in enduring disability, delayed functional recovery, and extended mechanical ventilation. Conventional clinical assessment tools capture only a limited scope of this multifactorial condition and often fail to accurately depict the nonlinear dynamics of physiological deterioration and recovery observed in critically ill patients. (2) Methods: This study presents an integrative framework that combines Physical and Rehabilitation Medicine (PRM) with analytical tools derived from nonlinear dynamics and fractal physiology. A prospective observational design and a long-term clinical evaluation were used along with nonlinear signal analysis. Fractal complexity metrics, including Higuchi fractal dimension (HFD) and detrended fluctuation analysis (DFA), were utilized to characterize the dynamics of neuromuscular and cardiorespiratory signals during rehabilitation. Clinical outcomes included the Medical Research Council (MRC) muscle strength score, the Functional Status Score for the ICU (FSS-ICU), and measures of respiratory performance. (3) Results: Early PRM intervention was associated with a consistent increase in neuromuscular strength, functional mobility, and respiratory muscle performance. Fractal analysis showed that physiological complexity was restored at the same time, as shown by large increases in HFD and DFA values. The recovery paths were not linear, and clustering analysis identified three distinct recovery phenotypes. (4) Conclusions: The integration of fractal biomarkers and nonlinear modeling into ICU rehabilitation may enable early risk stratification, improve the monitoring of functional recovery, and strengthen personalized rehabilitation strategies for patients with ICU-acquired weakness following severe COVID-19.