Several extensions of the standard model predict associated production of dark-matter particles with a Higgs boson. Such processes are searched for in final states with missing transverse momentum and a Higgs boson decaying to a b¯b pair with the ATLAS detector using 36.1  fb−1 of pp collisions at a center-of-mass energy of 13 TeV at the LHC. The observed data are in agreement with the standard model predictions and limits are placed on the associated production of dark-matter particles and a Higgs boson.