  In this paper, $f(R,T,R_{\mu\nu} T^{\mu\nu}$) gravity is considered. It is a
modified theory of gravity that exhibits a strong coupling of gravitational and
matter fields. Therefore, if gravity is governed by this model a number of
issues must be re-examined. In this context, the question of causality and its
violation is studied. Such analysis is carried out using the G\"{o}del-type
solutions. It is shown that this model allows both causal and non-causal
solutions. These solutions depend directly on the content of matter present in
the universe. For the non-causal solution, a critical radius is calculated,
beyond which causality is violated. Taking different matter contents, an
infinite critical radius emerges that leads to a causal solution. In this
causal solution, a natural relationship emerges between the parameters that
determine the matter considered.
