Background Physiological hyperarousal in social situations is a characteristic of individuals with social anxiety disorder (SAD), but so far it has been rarely studied as a biological risk for SAD. Here, we investigate whether children at high risk for SAD (because of their parents’ SAD) display physiological hyperarousal while interacting with a stranger. Also, we examine whether early physiological hyperarousal is related to later child social anxiety. Method One hundred and seventeen children took part in the stranger‐approach task when they were 2.5 and 4.5 years old. Heart rate (HR), heart rate variability (HRV), and electrodermal activity (EDA) were measured before, during, and after the conversation with a stranger. Both parents’ lifetime SAD status and SAD severity were assessed before the birth of the child. Both parents and children reported on children's social anxiety symptoms when children were 7.5. Results Children of parents with the lifetime SAD diagnosis did not differ in their physiological activity from children of parents without lifetime SAD. However, children of parents with more severe SAD displayed heightened EDA throughout the task procedure. Increased HR and reduced HRV during the stranger‐approach and elevated EDA throughout the task phases were linked to later child social anxiety. Conclusions Parents’ severity of SAD is related to child physiological hyperarousal early in their childhood. In addition, physiological hyperarousal in early childhood predicts later child social anxiety. Together, these findings suggest that early physiological hyperarousal in social situations may pose a risk for later child social anxiety and that physiological hyperarousal, and EDA in particular, may be a biological mechanism in the intergenerational transmission of SAD.