The interplay between topology and dissipation can give rise to a wealth of new phenomena and pave the way for novel topological lasers, sensors, and other quantum devices. Along these lines, we propose here an optomechanical setup in which the concomitant presence of a spatially modulated external drive and dissipation gives rise to a topologically nontrivial state for mechanical and optical excitations. We are able to show that the one-dimensional system considered here exhibits topologically protected end states for which mechanical and optical degrees of freedom are entangled. We show such entanglement to be robust with respect to the presence of nonzero-temperature baths and we propose a protocol for experimental observation of the entanglement.