Many studies have attempted to detect dementia in patients early by identifying certain prosodic and acoustic features during neuropsychological examinations. Conversational humanoid robots are expected to be used in elderly care to help increase their quality of life through interactions. If we can detect cognitive impairments from the elderly’s conversations with a robot, it would aid in early detection of dementia. In this study, we collected conversational data to simulate daily conversations with humanoid robots and compared them between healthy older adults and patients with mild cognitive impairments. This study evaluated multiple speech features and observed significant differences in answer length, response length, duration of utterance, jitter, and shimmer. Thus, the study results suggest the possibility of early detection of dementia through conversations with a humanoid robot.