Multimodal recommender systems improve the performance of canonical recommender systems with no item features by utilizing diverse content types such as text, images, and videos, while alleviating inherent sparsity of user-item interactions and accelerating user engagement. However, current neural network-based models often incur significant computational overhead due to the complex training process required to learn and integrate information from multiple modalities. To overcome this limitation, we propose MultiModal-Graph Filtering (MM-GF), a training-free method based on the notion of graph filtering (GF) for efficient and accurate multimodal recommendations. Specifically, MM-GF first constructs multiple similarity graphs through nontrivial multimodal feature refinement such as robust scaling and vector shifting by addressing the heterogeneous characteristics across modalities. Then, MM-GF optimally fuses multimodal information using linear low-pass filters across different modalities. Extensive experiments on real-world benchmark datasets demonstrate that MM-GF not only improves recommendation accuracy by up to 13.35% compared to the best competitor but also dramatically reduces computational costs by achieving the runtime of less than 10 seconds.