Consistent daily routines are associated with children’s well-being. Family routines provide both a predictable structure to guide behavior and an emotional environment that supports development. Enforcing family routines, improving family relationships, and creating a healthy home environment are necessary to maintain children’s psychosocial health. This study examined the associations between family routines, family relationships, and elementary school children’s behavior. Parents of 1515 third-grade students (8–9 years old) completed a self-administered questionnaire in Japan in 2017. We conducted a path analysis to examine the associations between the predictor variable of family routines, the mediating variable of family relationships, and the criterion variable of children’s behavior. A total of 717 valid responses were included in the analysis. The results showed that family routines were significantly related to children’s behavior (internalizing problem behaviors, externalizing problem behaviors, and prosocial behaviors) through family relationships (cohesiveness, expressiveness, and conflict). Family routines were positively associated with cohesiveness and expressiveness, and negatively associated with conflict. Cohesiveness was negatively associated with externalizing problem behaviors. While expressiveness was negatively associated with internalizing and externalizing problem behaviors, it was positively associated with prosocial behaviors. Conversely, conflict was positively associated with internalizing and externalizing problem behaviors, and negatively associated with prosocial behaviors. Our findings indicate that family routines may protect children’s mental health from the stressors of daily life and foster interpersonal and social competence. Moreover, family routines may stabilize family relationships, reduce children’s problem behaviors, and improve social competence.