Parkinson’s disease (PD) is a neurodegenerative disorder characterized by a range of motor and non-motor symptoms. One of the notable non-motor symptoms of PD is the presence of vocal disorders, attributed to the underlying pathophysiological changes in the neural control of the laryngeal and vocal tract musculature. From this perspective, the integration of machine learning (ML) techniques in the analysis of speech signals has significantly contributed to the detection and diagnosis of PD. Particularly, MEL Frequency Cepstral Coefficients (MFCCs) and Gammatone Frequency Cepstral Coefficients (GTCCs) are both feature extraction techniques commonly used in the field of speech and audio signal processing that could exhibit great potential for vocal disorder identification. This study presents a novel approach to the early detection of PD through ML applied to speech analysis, leveraging both MFCCs and GTCCs. The recordings contained in the Mobile Device Voice Recordings at King’s College London (MDVR-KCL) dataset were used. These recordings were collected from healthy individuals and PD patients while they read a passage and during a spontaneous conversation on the phone. Particularly, the speech data regarding the spontaneous dialogue task were processed through speaker diarization, a technique that partitions an audio stream into homogeneous segments according to speaker identity. The ML applied to MFCCS and GTCCs allowed us to classify PD patients with a test accuracy of 92.3%. This research further demonstrates the potential to employ mobile phones as a non-invasive, cost-effective tool for the early detection of PD, significantly improving patient prognosis and quality of life.