Tremor in Parkinson's disease (PD) is a fundamental feature used in the determination of disease onset and progression. Traditionally, tremor has been evaluated using frequency domain analysis. However, in many cases, this analysis did not show significant differences comparing healthy elders and individuals with PD. Given its complex nature, recently the interest in nonlinear dynamical analysis for better understanding of tremor has grown. In this paper, we examine the effect of PD on the complexity of the tremor time series of PD patients using the approximate entropy method (ApEn). Tremor was also evaluated in the frequency domain. This study involved 11 healthy and 11 PD patients. The peak frequency was similar in both groups, while the amplitude and power in the peak frequency and the total power were significantly higher in PD patients (p < 0.0001). A significant reduction (p < 0.001) in ApEn was observed in PD. ROC analysis showed that ApEn differentiated physiological tremor from tremor in PD patients with high accuracy. These results are in close agreement with pathophysiological fundamentals, and provide evidence that in PD patients the tremor pattern becomes less complex. Furthermore, our findings also suggest that ApEn has a high clinical potential in assessing PD patients.