The early identification of microvascular changes in patients with Coronavirus Disease 2019 (COVID-19) may offer an important clinical opportunity. This study aimed to define a method, based on deep learning approaches, for the identification of COVID-19 patients from the analysis of the raw PPG signal, acquired with a pulse oximeter. To develop the method, we acquired the PPG signal of 93 COVID-19 patients and 90 healthy control subjects using a finger pulse oximeter. To select the good quality portions of the signal, we developed a template-matching method that excludes samples corrupted by noise or motion artefacts. These samples were subsequently used to develop a custom convolutional neural network model. The model accepts PPG signal segments as input and performs a binary classification between COVID-19 and control samples. The proposed model showed good performance in identifying COVID-19 patients, achieving 83.86% accuracy and 84.30% sensitivity (hold-out validation) on test data. The obtained results indicate that photoplethysmography may be a useful tool for microcirculation assessment and early recognition of SARS-CoV-2-induced microvascular changes. In addition, such a noninvasive and low-cost method is well suited for the development of a user-friendly system, potentially applicable even in resource-limited healthcare settings.