  In this paper we investigate gravitational interactions of massive higher
spin fields in three dimensional $AdS$ space with arbitrary value of
cosmological constant including flat Minkowski space. We use frame-like gauge
description for such massive fields adopted to three-dimensional case. At
first, we carefully analyze the procedure of switching on gravitational
interactions in the linear approximation on the example of massive spin-3 field
and then proceed with the generalization to the case of arbitrary integer spin
field. As a result we construct a cubic interaction vertex linear in spin-2
field and quadratic in higher spin field on $AdS_3$ background. As in the
massless case the vertex does not contain any higher derivative corrections to
the Lagrangian and/or gauge transformations. Thus, even after switching on
gravitational interactions, one can freely consider any massless or partially
massless limits as well as the flat one.
