The radiological diagnosis of Crohn's disease (CD)-related anorectal cancer is difficult; it is often found in advanced stages and has a poor prognosis because of the difficulty of curative surgery. However, there are no studies on predicting the diagnosis of CD-related cancer. The present study aimed to develop a predictive model to diagnose CD cancerous lesions more accurately in a way that can be interpreted by clinicians. Patients with CD who developed anorectal CD lesions at Hyogo Medical University (Nishinomiya, Japan) between March 2009 and June 2022 were included in the present study. T2-weighted and T1-weighted magnetic resonance (MR) images were utilized for our analysis. Images of anorectal lesions were segmented using open-source 3D Slicer software, and radiomic features were extracted using PyRadiomics. Six machine learning models were investigated and compared: i) Support vector machine; ii) naive Bayes; iii) random forest; iv) light gradient boosting machine; v) extremely randomized trees; vi) and regularized greedy forest (RGF). SHapley Additive exPlanations (SHAP) values were calculated to assess the extent to which each radiomic feature contributed to the model's predictions compared to baseline, represented as the average of the model's predictions for all test data. The T2-weighted images of 28 patients with anorectal cancer and 40 non-cancer patients were analyzed and the contrast-enhanced T1-weighted images of 22 cancer and 40 non-cancer patients. The model with the highest area under the curve (AUC) was the RGF-based model constructed using T2-weighted image features, achieving an AUC of 0.944 (accuracy, 0.862; recall, 0.830). The SHAP-based model explanation suggested a strong association between the diagnosis of CD-related anorectal cancer and features such as complex lesion texture; greater pixel separation within the same coronal cross-section; larger, randomly distributed clumps of pixels with the same signal intensity; and a more spherical lesion shape on T2-weighted images. The MRI radiomics-based RGF model demonstrated outstanding performance in predicting CD-related anorectal cancer. These results may affect the diagnosis and surveillance strategies of CD-related colorectal cancer.