Background: Over the next 5 years, new breast cancer screening guidelines recommending magnetic resonance imaging (MRI) for certain patients will significantly increase the volume of imaging data to be analyzed. While this increase poses challenges for radiologists, artificial intelligence (AI) offers potential solutions to manage this workload. However, the development of AI models is often hindered by manual annotation requirements and strict data-sharing regulations between institutions. Methods: In this study, we present an integrated pipeline combining weakly supervised learning—reducing the need for detailed annotations—with local AI model training via swarm learning (SL), which circumvents centralized data sharing. We utilized three datasets comprising 1372 female bilateral breast MRI exams from institutions in three countries: the United States (US), Switzerland, and the United Kingdom (UK) to train models. These models were then validated on two external datasets consisting of 649 bilateral breast MRI exams from Germany and Greece. Results: Upon systematically benchmarking various weakly supervised two-dimensional (2D) and three-dimensional (3D) deep learning (DL) methods, we find that the 3D-ResNet-101 demonstrates superior performance. By implementing a real-world SL setup across three international centers, we observe that these collaboratively trained models outperform those trained locally. Even with a smaller dataset, we demonstrate the practical feasibility of deploying SL internationally with on-site data processing, addressing challenges such as data privacy and annotation variability. Conclusions: Combining weakly supervised learning with SL enhances inter-institutional collaboration, improving the utility of distributed datasets for medical AI training without requiring detailed annotations or centralized data sharing.