Multimodal emotion recognition (MER) aims to enhance the understanding of human emotions by integrating visual, auditory, and textual modalities. However, previous MER approaches often depend on a dominant modality rather than considering all modalities, leading to poor generalization. To address this, we propose Causal Inference in Multimodal Emotion Recognition (CausalMER), which leverages counterfactual reasoning and causal graphs to capture relationships between modalities and reduce direct modality effects contributing to bias. This allows CausalMER to make unbiased predictions while being easily applied to existing MER methods in a model-agnostic manner, without requiring any architectural modifications. We evaluate CausalMER on the IEMOCAP and CMU-MOSEI datasets, widely used benchmarks in MER, and compare it with existing methods. On the IEMOCAP dataset with the MulT backbone, CausalMER achieves an average accuracy of 83.4%. On the CMU-MOSEI dataset, the average accuracies with MulT, PMR, and DMD backbones are 50.1%, 48.8%, and 48.8%, respectively. Experimental results demonstrate that CausalMER is robust in missing modality scenarios, as shown by its low standard deviation in performance drop gaps. Additionally, we evaluate modality contributions and show that CausalMER achieves balanced contributions from each modality, effectively mitigating direct biases from individual modalities.