There is a critical need for fast, inexpensive, objective, and accurate screening tools for childhood psychopathology. Perhaps most compelling is in the case of internalizing disorders, like anxiety and depression, where unobservable symptoms cause children to go unassessed-suffering in silence because they never exhibiting the disruptive behaviors that would lead to a referral for diagnostic assessment. If left untreated these disorders are associated with long-term negative outcomes including substance abuse and increased risk for suicide. This paper presents a new approach for identifying children with internalizing disorders using an instrumented 90-second mood induction task. Participant motion during the task is monitored using a commercially available wearable sensor. We show that machine learning can be used to differentiate children with an internalizing diagnosis from controls with 81% accuracy (67% sensitivity, 88% specificity). We provide a detailed description of the modeling methodology used to arrive at these results and explore further the predictive ability of each temporal phase of the mood induction task. Kinematical measures most discriminative of internalizing diagnosis are analyzed in detail, showing affected children exhibit significantly more avoidance of ambiguous threat. Performance of the proposed approach is compared to clinical thresholds on parent-reported child symptoms which differentiate children with an internalizing diagnosis from controls with slightly lower accuracy (.68-.75 vs. .81), slightly higher specificity (.88-1.00 vs. .88), and lower sensitivity (.00-.42 vs. .67) than the proposed, instrumented method. These results point toward the future use of this approach for screening children for internalizing disorders so that interventions can be deployed when they have the highest chance for long-term success.