Cosmological and astrophysical observations indicate the existence of Dark Matter. Many beyond Standard Model theories predict associated production of Dark Matter particle candidates (WIMPs) with a Higgs boson at energies that can be probed at collider experiments like ATLAS. Initially, a brief and broad introduction to ATLAS and to the topic in question is provided. The presented search for Dark Matter produced in association with a Higgs boson decaying to a pair of b-quarks is performed using proton-proton collisions at a centre-of-mass energy of 13~TeV with an integrated luminosity of 36.1 fb^-1 recorded with the ATLAS detector at the Large Hadron Collider. Experimental sensitivity improvements are presented. The observed data are found to be in agreement with the Standard Model predictions. Upper limits on the production cross-section of a beyond Standard Model scenario are presented.