We focus on a modified version of the Horava–Lifshitz theory and, in particular, we consider the impact of its weak field static spherically symmetric limit on the galaxy dynamics. In a previous paper, we used the modified gravitational potential obtained in this theory to evaluate the Milky Way rotation curve using a spheroidal truncated power-law bulge and a double exponential disc as the only sources of the gravitational field, and showed that the modified rotation curve is not in agreement with the data. Making a step forward, we here include also the contribution from a dark matter halo in order to see whether this helps in fitting the rotation curve data. As a test case, we consider a sample of spiral galaxies with smooth baryon matter distribution and well-measured circular velocity profiles. It turns out that although a marginal agreement with the data can be found, this can only be obtained if the dark matter halo has an unrealistically small virial mass and incredibly large concentration. Such results can be interpreted as strong evidence against the reliability of the gravitational potential obtained in the modified version of the Horava–Lifshitz theory that we consider in this paper.