Appropriate intervention and care in detecting cognitive impairment early are essential to effectively prevent the progression of cognitive deterioration. Diagnostic voice analysis is a noninvasive and inexpensive screening method that could be useful for detecting cognitive deterioration at earlier stages such as mild cognitive impairment. We aimed to distinguish between patients with dementia or mild cognitive impairment and healthy controls by using purely acoustic features (i.e., nonlinguistic features) extracted from two simple phrases. Voice was analyzed on 195 recordings from 150 patients (age, 45–95 years). We applied a machine learning algorithm (LightGBM; Microsoft, Redmond, WA, USA) to test whether the healthy control, mild cognitive impairment, and dementia groups could be accurately classified, based on acoustic features. Our algorithm performed well: area under the curve was 0.81 and accuracy, 66.7% for the 3-class classification. Thus, our vocal biomarker is useful for automated assistance in diagnosing early cognitive deterioration.