A search for the exotic decay of the Higgs boson (H) into a b (b) overbar resonance plus missing transverse momentum is described. The searchis performed with the ATLAS detector at the Large Hadron Collider using139 fb(-1) of pp collisions at root s = 13 TeV. The search targetsevents from ZH production in an NMSSM scenario where H -> chi(similar to0)(2)chi(similar to 0)(1), with chi(similar to 0)(2) -> a chi(similar to0)(1), where a is a light pseudoscalar Higgs boson and chi(similar to0)(1,)(2) are the two lightest neutralinos. The decay of the a bosoninto a pair of b-quarks results in a peak in the dijet invariant massdistribution. The final-state signature consists of two leptons, two ormore jets, at least one of which is identified as originating from ab-quark, and missing transverse momentum. Observations are consistentwith Standard Model expectations and upper limits are set on the productof cross section times branching ratio for a three-dimensional scan ofthe masses of the chi(similar to 0)(2), chi(similar to 0)(1) and aboson.