Eye contact with a human and with a humanoid robot elicits attention- and affect-related psychophysiological responses. However, these responses have mostly been studied in adults, leaving their developmental origin poorly understood. In this study, 114 infants (6–8 months old) viewed direct and averted gaze directions of a live human and an embodied humanoid robot while their heart rate deceleration (attention orienting), skin conductance (affective arousal), and facial muscle activity (affective valence) were measured. In addition, a non-humanoid object (a vase) was used as a control stimulus. Infants’ attention orienting was stronger to averted versus direct gaze of a human and a robot, but indifferent to the averted versus direct orientation of the non-humanoid object. Moreover, infants’ attention orienting was equally intensive toward a human and a robot, but less intensive toward a non-humanoid object. Affective arousal was insensitive to gaze direction and did not differ between the human, the robot, and the non-humanoid object. Facial muscle responses showed sensitivity to the gaze direction of a human and of a robot but not to the orientation of the non-humanoid object. These results suggest that infants recognize the attentional and affective/affiliative significance not only in a human’s gaze but also in a robot’s gaze.