Multimodal emotion recognition (MMER) is an active research field that aims to accurately recognize human emotions by fusing multiple perceptual modalities. However, inherent heterogeneity across modalities introduces distribution gaps and information redundancy, posing significant challenges for MMER. In this paper, we propose a novel fine-grained disentangled representation learning (FDRL) framework to address these challenges. Specifically, we design modality-shared and modality-private encoders to project each modality into modality-shared and modality-private subspaces, respectively. In the shared subspace, we introduce a fine-grained alignment component to learn modality-shared representations, thus capturing modal consistency. Subsequently, we tailor a fine-grained disparity component to constrain the private subspaces, thereby learning modality-private representations and enhancing their diversity. Lastly, we introduce a fine-grained predictor component to ensure that the labels of the output representations from the encoders remain unchanged. Experimental results on the IEMOCAP dataset show that FDRL outperforms the state-of-the-art methods, achieving 78.34% and 79.44% on WAR and UAR, respectively.