Objective: Recent evidence showed that individuals with congenital face processing impairment (congenital prosopagnosia [CP]) are highly accurate when they have to recognize their own face (self-face advantage) in an implicit matching task, with a preference for the right-half of the self-face (right perceptual bias). Yet the perceptual strategies underlying this advantage are unclear. Here, we aimed to verify whether both the self-face advantage and the right perceptual bias emerge in an explicit task, and whether those effects are linked to a different scanning strategy between the self-face and unfamiliar faces. Method: Eye movements were recorded from 7 CPs and 13 controls, during a self/other discrimination task of stimuli depicting the self-face and another unfamiliar face, presented upright and inverted. Results: Individuals with CP and controls differed significantly in how they explored faces. In particular, compared with controls, CPs used a distinct eye movement sampling strategy for processing inverted faces, by deploying significantly more fixations toward the nose and mouth areas, which resulted in more efficient recognition. Moreover, the results confirmed the presence of a self-face advantage in both groups, but the eye movement analyses failed to reveal any differences in the exploration of the self-face compared with the unfamiliar face. Finally, no bias toward the right-half of the self-face was found. Conclusions: Our data suggest that the self-face advantage emerges both in implicit and explicit recognition tasks in CPs as much as in good recognizers, and it is not linked to any specific visual exploration strategies.