Mediation analysis is an approach for assessing the direct and indirect effects of an initial variable on an outcome through a mediator. In practice, mediation models can involve a censored mediator (eg, a woman's age at menopause). The current research for mediation analysis with a censored mediator focuses on scenarios where outcomes are continuous. However, the outcomes can be binary (eg, type 2 diabetes). Another challenge when analyzing such a mediation model is to use data from a case‐control study, which results in biased estimations for the initial variable‐mediator association if a standard approach is directly applied. In this study, we propose an approach (denoted as MAC‐CC) to analyze the mediation model with a censored mediator given data from a case‐control study, based on the semiparametric accelerated failure time model along with a pseudo‐likelihood function. We adapted the measures for assessing the indirect and direct effects using counterfactual definitions. We conducted simulation studies to investigate the performance of MAC‐CC and compared it to those of the naïve approach and the complete‐case approach. MAC‐CC accurately estimates the coefficients of different paths, the indirect effects, and the proportions of the total effects mediated. We applied the proposed and existing approaches to the mediation study of genetic variants, a woman's age at menopause, and type 2 diabetes based on a case‐control study of type 2 diabetes. Our results indicate that there is no mediating effect from the age at menopause on the association between the genetic variants and type 2 diabetes.