The appearance of colors can be affected by their spatiotemporal context. The shift in color appearance according to the surrounding colors is called color induction or chromatic induction; in particular, the shift in opponent color of the surround is called chromatic contrast. To investigate whether chromatic induction occurs even when the chromatic surround is imperceptible, we measured chromatic induction during interocular suppression. A multicolor or uniform color field was presented as the surround stimulus, and a colored continuous flash suppression (CFS) stimulus was presented to the dominant eye of each subject. The subjects were asked to report the appearance of the test field only when the stationary surround stimulus is invisible by interocular suppression with CFS. The resulting shifts in color appearance due to chromatic induction were significant even under the conditions of interocular suppression for all surround stimuli. The magnitude of chromatic induction differed with the surround conditions, and this difference was preserved regardless of the viewing conditions. The chromatic induction effect was reduced by CFS, in proportion to the magnitude of chromatic induction under natural (i.e., no-CFS) viewing conditions. According to an analysis with linear model fitting, we revealed the presence of at least two kinds of subprocesses for chromatic induction that reside at higher and lower levels than the site of interocular suppression. One mechanism yields different degrees of chromatic induction based on the complexity of the surround, which is unaffected by interocular suppression, while the other mechanism changes its output with interocular suppression acting as a gain control. Our results imply that the total chromatic induction effect is achieved via a linear summation of outputs from mechanisms that reside at different levels of visual processing.