The human eye-movement system is equipped with a sophisticated updating mechanism that can adjust for large retinal displacements produced by saccadic eye movements. The nature of this updating mechanism is still highly debated. Previous studies have demonstrated that updating can occur very rapidly and is initiated before the start of a saccade. In the present study, we used saccade curvature to demonstrate that the oculomotor system is tuned for detecting object displacements during saccades. Participants made a sequence of saccades while ignoring an irrelevant distractor. Curvature of the second saccade relative to the distractor was used to estimate the time course of updating. Saccade curvature away from the presaccadic location of the distractor emerged as early as 80 ms after the first saccade when the distractor was displaced during a saccade. This is about 50 ms earlier than when a distractor was only present before a saccade, only present after a saccade, or remained stationary across a saccade. This shows that the oculomotor system prioritizes detection of object displacements during saccades, which may be useful for guiding corrective saccades. The results also challenge previous views by demonstrating the additional role of postsaccadic information in updating target-distractor competition across saccades.