With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex interactions in the joint distribution of the variables to be estimated. After formally introducing the model and showing how it can be implemented, we carry out a simulation study and a real-data study in order to assess its performance and compare it with the commonly used listwise deletion and an available R-routine. Results indicate that the BMLC model is able to recover unbiased parameter estimates of the analysis models considered in our studies, as well as to correctly reflect the uncertainty due to missing data, outperforming the competing methods.