Multimodal MRI offers a comprehensive, non-invasive assessment of structure, which improves the diagnostic accuracy of brain tumor segmentation (BTS). BTS faces major challenges due to tumor heterogeneity, data quality, modality-specific information and algorithm complexity. Many existing methods do not utilize the complementary information available in multimodal data, as they depend on early fusion strategies and neglect modality-specific features. To overcome these issues, a novel architecture termed MAAF-Net: Modality-Adaptive Attention Fusion Network for 3D BTS has been proposed in this study. The MAAF-Net model preserves the semantic information of each MRI modality through modality-specific encoders (MSEnc). The extracted features are integrated using a Modality Attention Module (MAM). The MAM learns the context-dependent importance of each modality and adaptively reweights modality features during fusion. This fusion technique enables the model to focus on clinically relevant information while discarding redundant or less informative features. In addition, multi-scale supervision is incorporated to improve gradient flow and training stability. The MAAF-Net model is trained and validated on the BraTS 2024 benchmark dataset using five-fold cross-validation. The MAAF-Net achieves Dice scores of 0.92 for Tumor Core (TC) and 0.91 for Enhancing Tumor (ET) with HD95 values of 3.7 mm and 3.5 mm, respectively. Additionally, compared with early and attention-based fusion methods, MAAF-Net improves Dice scores by up to 8% for ET. Experimental findings from the ablation study further validate the effectiveness of the proposed model.