In this paper, we consider the G¨odel-type universes and study the issue of causality in a modified gravity with a non-minimal curvature-matter coupling within the Palatini approach. To examine the causality violation in this model, we assume two kinds of matter sources, a perfect fluid and a scalar field. We show that in the case of a perfect fluid, there exist a critical radius rc which beyond that the casuality is violated. On the other hand, assuming a scalar field as the matter source, the critical radius is being infinity thus the breakdown of causality is forbidden.
