Based on recent advances in non-linear analysis, the surface electromyography (sEMG) signal has been studied from the viewpoints of self-affinity and complexity. In this study, we examine usage of critical exponent analysis (CE) method, a fractal dimension (FD) estimator, to study properties of the sEMG signal and to deploy these properties to characterize different movements for gesture recognition. SEMG signals were recorded from thirty subjects with seven hand movements and eight muscle channels. Mean values and coefficient of variations of the CE from all experiments show that there are larger variations between hand movement types but there is small variation within the same type. It also shows that the CE feature related to the self-affine property for the sEMG signal extracted from different activities is in the range of 1.855~2.754. These results have also been evaluated by analysis-of-variance (p-value). Results show that the CE feature is more suitable to use as a learning parameter for a classifier compared with other representative features including root mean square, median frequency and Higuchi's method. Most p-values of the CE feature were less than 0.0001. Thus the FD that is computed by the CE method can be applied to be used as a feature for a wide variety of sEMG applications.