Adaptive adjustments of strategies are needed to optimize behavior in a dynamic and uncertain world. A key function in implementing flexible behavior and exerting self-control is represented by the ability to stop the execution of an action when it is no longer appropriate for the environmental requests. Importantly, stimuli in our environment are not equally relevant and some are more valuable than others. One example is the gaze of other people, which is known to convey important social information about their direction of attention and their emotional and mental states. Indeed, gaze direction has a significant impact on the execution of voluntary saccades of an observer since it is capable of inducing in the observer an automatic gaze-following behavior: a phenomenon named social or joint attention. Nevertheless, people can exert volitional inhibitory control on saccadic eye movements during their planning. Little is known about the interaction between gaze direction signals and volitional inhibition of saccades. To fill this gap, we administered a countermanding task to 15 healthy participants in which they were asked to observe the eye region of a face with the eyes shut appearing at central fixation. In one condition, participants were required to suppress a saccade, that was previously instructed by a gaze shift toward one of two peripheral targets, when the eyes were suddenly shut down (social condition, SC). In a second condition, participants were asked to inhibit a saccade, that was previously instructed by a change in color of one of the two same targets, when a change of color of a central picture occurred (non-social condition, N-SC). We found that inhibitory control was more impaired in the SC, suggesting that actions initiated and stopped by social cues conveyed by the eyes are more difficult to withhold. This is probably due to the social value intrinsically linked to these cues and the many uses we make of them.