  We study the RKKY interaction between two magnetic impurities located on the
surface of a three-dimensional Dirac semimetal with two Dirac nodes in the band
structure. By taking into account both bulk and surface contributions to the
exchange interaction between the localized spins, we demonstrate that the
surface contribution in general dominates the bulk one at distances larger than
the inverse node separation due to a weaker power-law decay. We find a strong
anisotropy of the surface term with respect to the spins being aligned along
the node separation axis or perpendicular to it. In the many impurity dilute
regime, this implies formation of quasi-one-dimensional magnetic stripes
orthogonal to the node axis. We also discuss the effects of a surface
spin-mixing term coupling electrons from spin-degenerate Fermi arcs.
