Despite the marked impact of the coronavirus disease 2019 (COVID-19) pandemic on the life of families and its possible negative implications for sleep, little is known about how sleep among parents and children has been impacted by this current crisis. In the present study, we addressed, for the first time, possible consequences of the COVID-19 crisis and home confinement on maternal anxiety, maternal insomnia, and maternal reports of sleep problems among children aged 6–72 months in Israel (N = 264). Our results revealed a high frequency of maternal clinical insomnia during the COVID-19 pandemic: 23% during the pandemic, compared to only 11% before the pandemic (retrospective reports about 1–2 months before the pandemic). About 80% of mothers reported mild-to-high levels of current COVID-19 anxiety. The majority of mothers reported no change in their child’s sleep quality, duration, and sleeping arrangement. However, about 30% reported a negative change in child’s sleep quality and a decrease in sleep duration, and there were also mothers who reported a positive change. These findings suggest that the changes in sleep patterns during the COVID-19 pandemic are varied and that no unified change for the worse should be expected. Further consideration of changes in sleep within the family context during this ongoing crisis is needed.