Graves’ disease has been reported to affect the clinical features of moyamoya disease (MMD), an occlusion of the circle of Willis. This study aimed to clarify the characteristics of MMD in patients with Graves’ disease. This was a single-center, retrospective study. The prevalence and clinical features of MMD patients among all patients with thyroid disease who visited Ito Hospital from January 2005 to December 2019 were evaluated. The relationship between MMD and hyperthyroidism was analyzed in new-onset Graves’ disease patients during the same period. Of all 394,422 patients with thyroid disease, 88,180 had Graves’ disease, and 40 had MMD with Graves’ disease, i.e., the prevalence was 45.36 per 100,000 patients with Graves’ disease (0.0454%). The median age at onset of MMD was 39 years (interquartile range, 31–54 years), with a male to female ratio of 1:12. The most common time that MMD was diagnosed was within 1 year after the onset of Graves’ disease, in 9 of 40 patients (22.5%), and 19 of 40 patients (47.5%) underwent bypass surgery for MMD. In MMD with Graves’ disease, headache was the most frequent symptom, and ischemic types of stroke and bilateral lesions were common. Of 23,347 patients with new-onset Graves’ disease, 7 were diagnosed with MMD and the incidence of MMD was 5.94 patients per 100,000 person-years. Most patients developed MMD symptoms during hyperthyroidism. Although MMD is a rare condition, it should be noted that it can occur with Graves’ disease.