Vision-Language Models (VLMs) like CLIP have demonstrated remarkable generalization in zero- and few-shot settings, but adapting them efficiently to decentralized, heterogeneous data remains a challenge. While prompt tuning has emerged as a popular parameter-efficient approach in personalized federated learning, existing methods often sacrifice generalization in favor of personalization, struggling particularly on unseen classes or domains. In this work, we propose pFedMMA, the first personalized federated learning framework that leverages multi-modal adapters for vision-language tasks. Each adapter contains modality-specific up- and down-projection layers alongside a globally shared projection that aligns cross-modal features. Our optimization strategy allows clients to locally adapt to personalized data distributions while collaboratively training the shared projection to improve global generalization. This design is also communication-efficient, as only the shared component is exchanged during communication rounds. Through extensive experiments across eleven datasets, including domain- and label-shift scenarios, we show that pFedMMA achieves state-of-the-art trade-offs between personalization and generalization, outperforming recent federated prompt tuning methods.