Robots are a new category of social agents that, thanks to their embodiment, can be used to train and support cognitive skills such as cognitive control. Several studies showed that cognitive control mechanisms are sensitive to affective states induced by humor, mood, and symbolic feedback such as monetary rewards. In the present study, we investigated whether the social gaze of a humanoid robot can affect cognitive control mechanisms. To this end, in two experiments, we evaluated both the conflict resolution and trial-by-trial adaptations during an auditory Simon task, as a function of the type of feedback participants received in the previous trial from the iCub robot, namely, mutual or avoiding gaze behaviour. Across three experiments, we compared the effect of mutual, avoiding (Exp1 and Exp2), and neutral (Exp3) gaze feedback between screen-based (Exp1) and physically embodied setups (Exp2 and Exp3). Results showed that iCub’s social gaze feedback modulated conflict resolution, but not conflict adaptations. Specifically, the Simon effect was increased following mutual gaze feedback from iCub. Moreover, the modulatory effect was observed for the embodied setup in which the robot could engage or avoid eye contact in real-time (Exp2) but not for the screen-based setting (Exp1). Our findings showed for the first time that social feedback in Human-Robot Interaction, such as social gaze, can be used to modulate cognitive control. The results highlight the advantage of using robots to evaluate and train complex cognitive skills in both healthy and clinical populations.