In the near future, ride-sharing vehicles are expected to serve a significant fraction of the transportation demands in cities and urban areas. In the past two decades, there has been an increased occurrence of highly infectious diseases like COVID-19 in the world. The simultaneous increase in ride-sharing penetration in the cities and the occurrence of infectious diseases around the world raise a question about the safety of ride-sharing vehicles amid an infectious disease outbreak. In this paper, we investigate the role of ride-sharing vehicles in the spread of COVID-19 in metropolitan areas. To this end, we considered a compartmental model to capture the progression of SARS-CoV-2 infections in an urban population and an agent-based simulation to capture the ride-sharing exposure to the disease. It is shown through the simulation that in the absence of any within-vehicle disease-control measures, ride-sharing can aggravate the spread of disease. Furthermore, it is shown that effective implementation of disease outbreak control measures at the ride-sharing level can almost nullify this aggravation.