Novel coronavirus disease 2019 (COVID-19) causes pulmonary and cardiovascular disorders and has become a worldwide emergency. Myocardial injury can be caused by direct or indirect damage, particularly mediated by a cytokine storm, a disordered immune response that can cause myocarditis, abnormal coagulation, arrhythmia, acute coronary syndrome, and myocardial infarction. The present review focuses on the mechanisms of this viral infection, cardiac biomarkers, consequences, and the possible therapeutic role of purinergic and adenosinergic signalling systems. In particular, we focus on the interaction of the extracellular nucleotide adenosine triphosphate (ATP) with its receptors P2X1, P2X4, P2X7, P2Y1, and P2Y2 and of adenosine (Ado) with A2A and A3 receptors, as well as their roles in host immune responses. We suggest that receptors of purinergic signalling could be ideal candidates for pharmacological targeting to protect against myocardial injury caused by a cytokine storm in COVID-19, in order to reduce systemic inflammatory damage to cells and tissues, preventing the progression of the disease by modulating the immune response and improving patient quality of life.