Online platforms collect rich information about participants and then share some of this information back with them to improve market outcomes. In this paper, we study the following information disclosure problem in two-sided markets: if a platform wants to maximize revenue, which sellers should the platform allow to participate, and how much of its available information about participating sellers' quality should the platform share with buyers? We study this information disclosure problem in the context of two distinct two-sided market models: one in which the platform chooses prices and the sellers choose quantities (similar to ride sharing), and one in which the sellers choose prices (similar to e-commerce). Our main results provide conditions under which simple information structures commonly observed in practice, such as banning certain sellers from the platform and not distinguishing between participating sellers, maximize the platform's revenue. The platform's information disclosure problem naturally transforms into a constrained price discrimination problem in which the constraints are determined by the equilibrium outcomes of the specific two-sided market model being studied. We analyze this constrained price discrimination problem to obtain our structural results.