Parkinson's disease (PD) is a progressive neurological disorder which affects the motor system. The automatic detection of PD improves the diagnosis of the disease, and it can be done in a non-invasive manner from speech. In this paper, we investigate the use of an exemplar-based sparse representation (SR) classification approach for detecting PD from speech. Exemplars are speech feature vectors extracted from the training data. The idea is to formulate the detection task as a problem of finding sparse representations of test speech feature vectors with respect to training speech exemplars. The main advantage of using the SR approach instead of conventional machine learning (ML)-based approaches is that the training step-which is time-consuming and sometimes requires unorganized hyperparameter tuning-is not needed. Furthermore, SRs are more robust to redundancy and noise in the data. In this work, we study SR classification approaches based on two sparse coding models, namely, l1-regularized least squares (l1LS) and nonnegative least squares (NNLS). We propose a strategy based on class-specific dictionaries for improving performance of the l1LS-and NNLS-based SR classification. To investigate the detection performance, the l1LS-and NNLS-based approaches are applied and compared with the traditional PD detection approach based on ML classification algorithms using the PC-GITA PD dataset and an openly available dataset consisting of mobile device voice recordings from healthy and PD patients. The results indicate that the proposed NNLS-based SR classification approach performs better than the traditional ML-based methods in discriminating PD patients from healthy subjects.