Infant sleep problems have been associated with a myriad of adverse child and parent outcomes, yet whether these problems may pose a risk for parents on the road has received little research attention. This study sought to test whether mothers of infants with insomnia are at an elevated risk for vehicular crashes, by comparing their objectively measured driving performance with that of mothers of well-sleeping infants and with that of women without children. Fifty-four women from these three groups completed a simulated driving task. Outcome measures included standard deviation of lateral position, number of lane crossings, standard deviation of speed, average speed and maximum speed. Women additionally reported on their driving behaviour using the Driving Behaviour Questionnaire, and on sleep, sleepiness and insomnia symptoms using 7-day sleep diaries and questionnaires. Mothers of infants with insomnia demonstrated greater lane deviation (Wald = 9.53, p = 0.009), higher maximum speed (Wald = 6.10, p = 0.04) and poorer self-rated driving behaviour (Wald = 7.44, p = 0.02) compared with control groups. Analyses also indicated that driving performance in mothers of infants with insomnia tended to be poorer relative to control groups with the progression of time on task. While further research is needed to assess the scope of these effects, our findings suggest that parents, healthcare providers and policymakers should be aware of the potential consequences of infant sleep problems on road safety, and collaborate to establish strategies to mitigate these risks.