Non-invasive prediction of isocitrate dehydrogenase (IDH) genotype plays an important role in tumor glioma diagnosis and prognosis. Recently, research has shown that radiology images can be a potential tool for genotype prediction, and fusion of multi-modality data by deep learning methods can further provide complementary information to enhance prediction accuracy. However, it still does not have an effective deep learning architecture to predict IDH genotype with three-dimensional (3D) multimodal medical images. In this paper, we proposed a novel multimodal 3D DenseNet (M3D-DenseNet) model to predict IDH genotypes with multimodal magnetic resonance imaging (MRI) data. To evaluate its performance, we conducted experiments on the BRATS-2017 and The Cancer Genome Atlas breast invasive carcinoma (TCGA-BRCA) dataset to get image data as input and gene mutation information as the target, respectively. We achieved 84.6% accuracy (area under the curve (AUC) = 85.7%) on the validation dataset. To evaluate its generalizability, we applied transfer learning techniques to predict World Health Organization (WHO) grade status, which also achieved a high accuracy of 91.4% (AUC = 94.8%) on validation dataset. With the properties of automatic feature extraction, and effective and high generalizability, M3D-DenseNet can serve as a useful method for other multimodal radiogenomics problems and has the potential to be applied in clinical decision making.