Federated learning (FL) has attracted considerable interest in the medical domain due to its capacity to facilitate collaborative model training while maintaining data privacy. However, conventional FL methods typically necessitate multiple communication rounds, leading to significant communication overhead and delays, especially in environments with limited bandwidth. One-shot federated learning addresses these issues by conducting model training and aggregation in a single communication round, thereby reducing communication costs while preserving privacy. Among these, one-shot federated ensemble learning combines independently trained client models using ensemble techniques such as voting, further boosting performance in non-IID data scenarios. On the other hand, existing machine learning methods in healthcare predominantly use unimodal data (e.g., medical images or textual reports), which restricts their diagnostic accuracy and comprehensiveness. Therefore, the integration of multi-modal data is proposed to address these shortcomings. In this paper, we introduce FedMME, an innovative one-shot multi-modal federated ensemble learning framework that utilizes multi-modal data for medical image analysis. Specifically, FedMME capitalizes on vision large language models to produce textual reports from medical images, employs a BERT model to extract textual features from these reports, and amalgamates these features with visual features to improve diagnostic accuracy. Experimental results show that our method demonstrated superior performance compared to existing one-shot federated learning methods in healthcare scenarios across four datasets with various data distributions. For instance, it surpasses existing one-shot federated learning approaches by more than 17.5% in accuracy on the RSNA dataset when applying a Dirichlet distribution with ($α$ = 0.3).