To establish a perceptually stable world despite the large retinal shifts caused by saccadic eye movements, the visual system reduces its sensitivity to the displacement of visual stimuli during saccades (e.g. saccadic suppression of displacement, SSD). Previous studies have demonstrated that inserting a temporal blank right after a saccade improves displacement detection performance. This 'blanking effect' suggests that visual information right after the saccade may play an important role in SSD. To understand the mechanisms underlying SSD, we here compare the effect of pre- and post-saccadic stimulus contrast on displacement detection during a saccade with and without inserting a blank. Our results show that observers' sensitivity to detect visual displacement was reduced by increasing post-saccadic stimulus contrast, but a blank relieves the impairment. We successfully explain the results with a model proposing that parvo-pathway signals suppress the magno-pathway processes responsible for detecting displacements across saccades. Our results suggest that the suppression of the magno-pathway by parvo-pathway signals immediately after a saccade causes SSD, which helps to achieve the perceptual stability of the visual world across saccades.