Multiplex networks have been proposed as an effective abstract of real complex systems, ranging from multi-modal urban transportation systems to communication systems. In this paper, we investigate a traffic-driven epidemic model in multiplex networks, and derive a theoretical approach to accurately predict the epidemic threshold of each layer. Our results show that the multiplex structure can produce different effects on the epidemic threshold of layers. Interestingly, one important finding is that the epidemic can be completely suppressed in a certain layer. This phenomenon occurs only when the connectivity of layers is very different, and the traffic flow is heterogeneously distributed over the layers. Therefore, epidemic spreading becomes quite distinct among the layers with different amounts of traffic flow. By using mean-field analysis, an explicit expression is derived to detect this traffic-induced epidemic suppression phenomenon. The accuracy of theoretical prediction is assessed in Erdős–Rényi and scale-free multiplex networks.