Background: The aim of this study was to assess changes in physical activity, screen time and sleep duration of preschoolers, children and adolescents and the prevalence of meeting the 24-h movement guidelines during the lockdown caused by COVID-19 in a sample from Spain and Brazil. Methods: A total of 1099 preschoolers, children and adolescents (aged 3–17 years) from Spain (12.1 ± 4.6 years) and Brazil (10.7 ± 4.3 years) were included. An online survey was created and distributed in each country using a snowball sampling strategy. This online survey was completed by parents (mother/father/responsible guardian). Results: The proportion of the sample who met the PA and ST recommendations decreased during the COVID-19 lockdown in both Spanish and Brazilian samples (p < 0.001), while sleep duration increased (p < 0.001). The proportion of the sample meeting the overall 24-h movement guidelines was very low before the lockdown (Spain 3.0%; Brazil 11.7%) and even worse during the lockdown (Spain 0.3%; Brazil 7.5%). Conclusions: The prevalence of preschoolers, children and adolescents in both the Spain and Brazil samples meeting the 24-h movement guidelines during COVID-19 restrictions was as low as previous studies in other countries. Efforts to protect and support healthy behaviors of young people during a period of pandemic restrictions need to be a priority.