The aim was to examine the sociodemographic predictors associated with changes in movement behaviors (physical activity, screen time, and sleep) among toddlers and preschoolers during the early stages of the coronavirus disease 2019 pandemic in Chile. Caregivers of 1- to 5-year-old children completed an online survey between 30 March and 27 April 2020. Information about the child’s movement behaviors before (retrospectively) and during the pandemic, as well as family characteristics were reported. In total, 3157 participants provided complete data (mean children age: 3.1 ± 1.38 years). During early stages of the pandemic, time spent in physical activity decreased, recreational screen time and sleep duration increased, and sleep quality declined. Toddlers and preschoolers with space to play at home and living in rural areas experienced an attenuated impact of the pandemic restrictions on their physical activity levels, screen time, and sleep quality. Older children, those whose caregivers were aged ≥35–<45 years and had a higher educational level, and those living in apartments had greater changes, mainly a decrease in total physical activity and increase in screen time. This study has shown the significant impact of the pandemic restrictions on movement behaviors in toddlers and preschoolers in Chile.