Background: With the rapid growth of the older adult population worldwide, car accidents involving this population group have become an increasingly serious problem. Cognitive impairment, which is assessed using neuropsychological tests, has been reported as a risk factor for being involved in car accidents; however, it remains unclear whether this risk can be predicted using daily behavior data. Objective: The objective of this study was to investigate whether speech data that can be collected in everyday life can be used to predict the risk of an older driver being involved in a car accident. Methods: At baseline, we collected (1) speech data during interactions with a voice assistant and (2) cognitive assessment data-neuropsychological tests (Mini-Mental State Examination, revised Wechsler immediate and delayed logical memory, Frontal Assessment Battery, trail making test-parts A and B, and Clock Drawing Test), Geriatric Depression Scale, magnetic resonance imaging, and demographics (age, sex, education)-from older adults. Approximately one-and-a-half years later, we followed up to collect information about their driving experiences (with respect to car accidents) using a questionnaire. We investigated the association between speech data and future accident risk using statistical analysis and machine learning models. Results: We found that older drivers (n=60) with accident or near-accident experiences had statistically discernible differences in speech features that suggest cognitive impairment such as reduced speech rate (P=.048) and increased response time (P=.040). Moreover, the model that used speech features could predict future accident or near-accident experiences with 81.7% accuracy, which was 6.7% higher than that using cognitive assessment data, and could achieve up to 88.3% accuracy when the model used both types of data. Conclusions: Our study provides the first empirical results that suggest analysis of speech data recorded during interactions with voice assistants could help predict future accident risk for older drivers by capturing subtle impairments in cognitive function.