Child sleep disorders are increasingly prevalent and understanding early predictors of sleep problems, starting in utero, may meaningfully guide future prevention efforts. Here, we investigated whether prenatal exposure to maternal psychological stress is associated with increased sleep problems in toddlers. We also examined whether fetal brain connectivity has direct or indirect influence on this putative association. Pregnant women underwent fetal resting-state functional connectivity MRI and completed questionnaires on stress, worry, and negative affect. At 3-year follow-up, 64 mothers reported on child sleep problems, and in the subset that have reached 5-year follow-up, actigraphy data (N = 25) has also been obtained. We observe that higher maternal prenatal stress is associated with increased toddler sleep concerns, with actigraphy sleep metrics, and with decreased fetal cerebellar-insular connectivity. Specific mediating effects were not identified for the fetal brain regions examined. The search for underlying mechanisms of the link between maternal prenatal stress and child sleep problems should be continued and extended to other brain areas.