In this paper we systematically construct simply transitive homogeneous
spacetime solutions of the three-dimensional Minimal Massive Gravity (MMG)
model. In addition to those that have analogs in Topologically Massive Gravity,
such as warped AdS and pp-waves, there are several solutions genuine to MMG.
Among them, there is a stationary Lifshitz metric with the dynamical exponent
z=-1 and an anisotropic Lifshitz solution where all coordinates scale
differently. Moreover, we identify a homogeneous Kundt type solution at the
chiral point of the theory. We also show that in a particular limit of the
physical parameters in which the Cotton tensor drops out from the MMG field
equation, homogeneous solutions exist only at the merger point in the parameter
space if they are not conformally flat.