A search for the exotic decay of the Higgs boson (H) into a b¯b resonance plus missing transverse momentum is described. The search is performed with the ATLAS detector at the Large Hadron Collider using 139 fb−1 of pp collisions at √s = 13 TeV. The search targets events from ZH production in an NMSSM scenario where H → χ˜02χ˜01, with χ˜02 → aχ˜01, where a is a light pseudoscalar Higgs boson and χ˜01,2 are the two lightest neutralinos. The decay of the a boson into a pair of b-quarks results in a peak in the dijet invariant mass distribution. The final-state signature consists of two leptons, two or more jets, at least one of which is identified as originating from a b-quark, and missing transverse momentum. Observations are consistent with Standard Model expectations and upper limits are set on the product of cross section times branching ratio for a threedimensional scan of the masses of the χ˜02, χ˜01 and a boson.