Brain-to-brain synchrony has been proposed as an important mechanism underlying social interaction. While first findings indicate that it may be modulated in children with autism spectrum disorder (ASD), no study to date has investigated the influence of different interaction partners and task characteristics. Using functional near-infrared spectroscopy hyperscanning, we assessed brain-to-brain synchrony in 41 male typically developing (TD) children (8–18 years; control sample), as well as 18 children with ASD and age-matched TD children (matched sample), while performing cooperative and competitive tasks with their parents and an adult stranger. Dyads were instructed either to respond jointly in response to a target (cooperation) or to respond faster than the other player (competition). Wavelet coherence was calculated for oxy- and deoxyhemoglobin brain signals. In the control sample, a widespread enhanced coherence was observed for parent–child competition, and a more localized coherence for parent–child cooperation in the frontopolar cortex. While behaviorally, children with ASD showed a lower motor synchrony than children in the TD group, no significant group differences were observed on the neural level. In order to identify biomarkers for typical and atypical social interactions in the long run, more research is needed to investigate the neurobiological underpinnings of reduced synchrony in ASD.