Mixtures of factor analyzers (MFA) provide a promising tool for modeling and clustering high-dimensional data that contain an overwhelmingly large number of attributes measured on individuals arisen from a heterogeneous population. Due to the restriction of experimental apparatus, measurements can be limited to some lower and/or upper detection bounds and thus the data are possibly censored. In this paper, we extend the MFA to accommodate censored data, and the new model is called the MFA with censoring (MFAC). A computationally feasible alternating expectation conditional maximization (AECM) algorithm is developed to carry out maximum likelihood estimation of the MFAC model. Practical issues related to model-based clustering and recovery of censored data are also discussed. Simulation studies are conducted to examine the effect of censoring in classification, estimation and cluster validation. We also present an application of the proposed approach to two real data examples in which a certain number of left-censored observations are present.