Background Executive dysfunction (ED) is often observed in subjects diagnosed with obstructive sleep apnea (OSA), but their assessment requires facilities that are not always available. We aim to evaluate the extent to which Frontal Assessment Battery (FAB) discriminates ED in newly diagnosed, untreated, and without-comorbidity OSA patients. Methods Sixty subjects participated in the study. Of these, 40 (31 males and 9 females) were newly diagnosed for OSA through full-night polysomnography (apnea/hypopnea index; M = 39.01, SD = 27.16), untreated, with a mean age of 54.50 years (SD = 8.90), while the remaining 20 (15 males and 5 females) had no symptoms of OSA (M = 51.60 years, SD = 10.70). The instruments used were the following: Questionnaire for Sleep Apnea Risk, Epworth Sleepiness Scale, Mini-Mental State Examination, and FAB. Results The group with OSA exhibited significantly lower values in the FAB global score (p = 0.003) and in Conceptualization (p = 0.001) and Mental Flexibility (p = 0.009) subtests. ROC analysis showed adequate discriminative capacity for the FAB global score (AUC = 0.74) and for Conceptualization (AUC = 0.75) and Mental Flexibility (AUC = 0.70) scores. Conclusions The FAB is a short and no-time-consuming tool that can be used to investigate the presence of ED in untreated OSA patients with no comorbidities, providing clinicians with a simple and effective way of detecting the presence of this dysfunction and allowing a more informed decision for the need of a full neuropsychological assessment.