Convolutional neural networks (CNNs) for brain tumor segmentation are generally developed using complete sets of magnetic resonance imaging (MRI) sequences for both training and inference. As such, these algorithms are not trained for realistic, clinical scenarios where parts of the MRI sequences which were used for training, are missing during inference. To increase clinical applicability, we proposed a cross-modal distillation approach to leverage the availability of multi-sequence MRI data for training and generate an enriched CNN model which uses only single-sequence MRI data for inference but outperforms a single-sequence CNN model. We assessed the performance of the proposed method for whole tumor and tumor core segmentation with multi-sequence MRI data available for training but only T1- weighted (T1w) sequence data available for inference, using both BraTS 2018, and in-house datasets. Results showed that cross-modal distillation significantly improved the Dice score for both whole tumor and tumor core segmentation when only T1w sequence data were available for inference. For the evaluation using the in-house dataset, cross-modal distillation achieved an average Dice score of 79.04% and 69.39% for whole tumor and tumor core segmentation, respectively, while a single-sequence U-Net model using T1w sequence data for both training and inference achieved an average Dice score of 73.60% and 62.62%, respectively. These findings confirmed cross-modal distillation as an effective method to increase the potential of single-sequence CNN models such that segmentation performance is less compromised by missing MRI sequences or having only one MRI sequence available for segmentation.