Reducing the representational discrepancy between source and target domains is a key component to maximize the model generalization. In this work, we advocate for leveraging natural language supervision for the domain generalization task. We introduce two modules to ground visual representations with texts containing typical reasoning of humans (1) Visual and Textual Joint Embedder and (2) Textual Explanation Generator. The former learns the image-text joint embedding space where we can ground high-level class-discriminative information into the model. The latter leverages an explainable model and generates explanations justifying the rationale behind its decision. To the best of our knowledge, this is the first work to leverage the vision-and-language cross-modality approach for the domain generalization task. Our experiments with a newly created CUB-DG benchmark dataset demonstrate that cross-modality supervision can be successfully used to ground domain-invariant visual representations and improve the model generalization. Furthermore, in the large-scale DomainBed benchmark, our proposed method achieves state-of-the-art results and ranks 1st on four out of five benchmarks.