In this paper we study the interplay between epidemic spreading and risk perception on multiplex networks. The basic idea is that the effective infection probability is affected by the perception of the risk of being infected, which we assume to be related to the fraction of infected neighbors, as introduced by Bagnoli et al. [Phys. Rev. E 76, 061904 (2007)PLEEE81539-375510.1103/PhysRevE.76.061904]. We rederive previous results using a self-organized method that automatically gives the percolation threshold in just one simulation. We then extend the model to multiplex networks considering that people get infected by physical contacts in real life but often gather information from an information network, which may be quite different from the physical ones. The similarity between the physical and the information networks determines the possibility of stopping the infection for a sufficiently high precaution level: if the networks are too different, there is no means of avoiding the epidemics.