Mounting evidence suggests that individuals with fibromyalgia (FM) have impairments in general cognitive functions. However, few studies have explored the possibility of dissociation between verbal and visuospatial memory impairments in FM. Therefore, the purpose of this study was to investigate the asymmetrical impairment of cognitive functions between verbal and visuospatial memory and between short-term and long-term memory. Neuropsychological assessments were carried out on 23 female patients with FM and 24 healthy female controls. Verbal memory abilities were assessed using the Korean version of the Rey auditory verbal learning test (KAVLT) and digit span task, and visuospatial memory abilities were assessed using the Korean version of the Rey complex figure test (KCFT) and spatial span task. The analysis of covariance was used to assess group differences in performance on cognitive tests after controlling for depression. The two groups did not significantly differ in terms of age, years of education, or in their estimated verbal and performance IQ, but FM patients reported more severe depressive symptoms than did controls on the Beck depression inventory. Significant group differences were found in immediate and delayed recall on the KCFT (F (1,44) = 6.49, p = 0.014 and F (1,44) = 6.96, p = 0.011, respectively), whereas no difference was found in immediate and delayed recall on the KAVLT. In terms of short-term memory, neither the digit span task nor spatial span task showed any difference between groups, regardless of whether repetition was forward or backward. These findings suggest that spatial memory abilities may be more impaired than verbal memory abilities in patients with FM.