  For the accurate understanding of compact objects such as neutron stars and
strange stars, the Tolmann-Openheimer-Volkof (TOV) equation has proved to be of
great use. Hence, in this work, we obtain the TOV equation for the
energy-momentum-conserved $f(R,T)$ theory of gravity to study strange quark
stars. The $f(R,T)$ theory is important, especially in cosmology, because it
solves certain incompleteness of the standard model. In general, there is no
intrinsic conservation of the energy-momentum tensor in the $f(R,T)$ gravity.
Since this conservation is important in the astrophysical context, we impose
the condition $\nabla T_{\mu\nu}=0$, so that we obtain a function $f(R,T)$ that
implies conservation. This choice of a function $f(R,T)$ that conserves the
momentum-energy tensor gives rise to a strong link between gravity and the
microphysics of the compact object. We obtain the TOV by taking into account a
linear equation of state to describe the matter inside strange stars, such as
$p=\omega\rho$ and the MIT bag model $p=\omega(\rho-4B)$. With these
assumptions it was possible to derive macroscopic properties of these objects.
