Parkinson’s disease (PD) is a neurodegenerative disease, that is mainly manifested by motor disorders worsening over time. Usually, the diagnosis is made if the examiner observes at least two of the following three symptoms: akinesia, rigidity, and tremors at rest. Unfortunately, these motor symptoms only appear after the loss of 50 to 60% of the dopaminergic neurons in the substantia nigra. A major research challenge is therefore to find ways to detect the disease earlier, to eventually be able to slow down, or even stop its progression from the start. Among the various clinical manifestations of this disease, the modification of the voice of the patients seems to be an element of interest in several respects. In this paper, we investigate and analyze the effectiveness of voice analysis to accurately detect the PD stages based on the Hoehn and Yahr (H&Y) scale. The voice pitch, Mel-frequency cepstral coefficients (MFCC), and gammatone cepstral coefficients (GTCC) are extracted from the voice of the patients, and the most pertinent features are selected by feature selection (FS) algorithms such as the minimum redundancy maximum relevance (mRMR) and ReliefF. These features are mapped to different classifiers to predict the PD stage automatically. The highest f1-score of 98.7% was achieved by 10 features selected using ReliefF and the support vector machine (SVM). The minimum redundancy maximum relevance (mRMR) combined with the SVM obtained a similar performance of 98.4% f1-score. The goal of this study is to build an inexpensive and accessible tool for remote patient monitoring.