During saccadic eye movements, the processing of visual information is transiently interrupted by a mechanism known as "saccadic suppression" [1] that is thought to ensure perceptual stability [2]. If, as proposed in the premotor theory of attention [3], covert shifts of attention rely on sub-threshold recruitment of oculomotor circuits, then saccadic suppression should also occur during covert shifts. In order to test this prediction, we designed two experiments in which participants had to orient towards a cued letter, with or without saccades. We analyzed the time course of letter identification score in an "attention" task performed without saccades, using the saccadic latencies measured in the "saccade" task as a marker of covert saccadic preparation. Visual conditions were identical in all tasks. In the "attention" task, we found a drop in perceptual performance around the predicted onset time of saccades that were never performed. Importantly, this decrease in letter identification score cannot be explained by any known mechanism aligned on cue onset such as inhibition of return, masking, or microsaccades. These results show that attentional allocation triggers the same suppression mechanisms as during saccades, which is relevant during eye movements but detrimental in the context of covert orienting.