Higher injury rates among children is a significant post-COVID-19 phenomenon. This paper focuses on injury frequency in pre-school, as well as in younger school-age children, and maps the approaches used by families to prevent injuries and ensure child safety in the Czech Republic. The aim of the survey was to determine what types of serious injuries prevail among children, how parents or grandparents evaluate the awareness of children toward dangerous situations, and what opinions and preferences they have regarding educating their children about health and safety. The questionnaire survey among parents and grandparents (N = 278) of children from birth to the age of 12 was conducted at educational events for the wider public in 2017–2019. The survey showed that head injuries (27%) are prevalent among pre-school children; however, in children older than 5 years, injuries are due to increased outdoor activity and tend to be more associated with sports and leisure activities (fractures 31%, burns 23%). Most respondents considered their children to be more likely to recognize life-threatening risks, which is worrying in the context of the rising number of injuries in the Czech Republic in recent years.