Considering that people with Parkinson’s disease (PD) experience challenges in the control of both balance and eye movements, this study investigated the effects of saccadic eye movements on body sway in people with PD in two bases of support positions (side-by-side and tandem stances). Ten people with PD and 11 healthy individuals performed (a) fixation; (b) horizontal saccadic eye movements to the right and left; and (c) vertical saccadic eye movements up and down. The protocol for each postural task consisted of one block of six trials, making a total of 12 trials. Body sway and gaze parameters were measured during the trials. In both people with PD and healthy individuals, anterior–posterior body sway was significantly reduced in horizontal saccadic eye movements in contrast to fixation, regardless of the body position (side-by-side and tandem stances). Furthermore, vertical saccadic eye movements increased the area of sway in contrast to horizontal ones (and not to fixation) in people with PD. In addition, people with PD showed a higher number of fixations in all experimental conditions, without changes in the mean duration of fixations in both body positions. In conclusion, individuals with PD can improve body sway by coupling eye movements and postural sway when performing horizontal saccadic eye movements but not when performing vertical saccadic eye movements.