The literature has long recognized that parental emotional competence, that is, the ability to express, understand, and regulate emotions, plays a key role in children’s development from early childhood. Nevertheless, the effect of parental alexithymia, which can be understood as a deficit in emotional competence, has not been thoroughly studied. In particular, the association between paternal alexithymia and behavioral problems in young children is still a neglected area of research. This study aims to investigate the association between paternal alexithymia and children’s internalizing and externalizing problems during the first three years of life, including whether overreactive parenting practices mediate the effect of alexithymia on children’s behavioral problems. A sample of 203 fathers of children aged 18–36 months were administered the TAS-20, the Overreactivity subscale of the Parenting Scale, and the Child Behavior Checklist (CBCL)/1½-5. The data indicate that paternal alexithymia is a predictor of children’s internalizing and externalizing behavioral problems and that paternal overreactivity mediates the effect of alexithymia. These results highlight the importance of preventing parental alexithymia and involving fathers in parenting support programs aimed at ensuring children’s mental health and adjustment.