  In this Letter we construct the noncommutative (NC) gravity model on the
$\theta$-constant NC space-time. We start from the NC $SO(2,3)_\star$ gauge
theory and use the enveloping algebra approach and the Seiberg-Witten map to
construct the effective NC gravity action. The action and the equations of
motion are expanded up to second order in the deformation parameter. The
equations of motion show that the noncommutativity plays a role of a source for
the curvature and/or torsion. Finally, we calculate the NC corrections to the
Minkowski space-time and we show that in the presence of noncommutativity
Minkowski space-time becomes curved, but remains torsion-free. The breaking of
diffeomorphism invariance is understood in terms of the preferred coordinate
system. We show that the coordinates we are using are the Fermi normal
coordinates. This suggests that the natural coordinate system in which one
should study NC gravity is given by the Fermi normal coordinates.
