Domain generalizability is a crucial aspect of a deep learning model since it determines the capability of the model to perform well on data from unseen domains. However, research on the domain generalizability of deep learning models for vision-language tasks remains limited, primarily because of the lack of required datasets. To address these challenges, we propose VolDoGer: Vision-Language Dataset for Domain Generalization, a dedicated dataset designed for domain generalization that addresses three vision-language tasks: image captioning, visual question answering, and visual entailment. We constructed VolDoGer by extending LLM-based data annotation techniques to vision-language tasks, thereby alleviating the burden of recruiting human annotators. We evaluated the domain generalizability of various models, ranging from fine-tuned models to a recent multimodal large language model, through VolDoGer.