The influence of microstructural changes induced by heat treatment on fracture toughness is investigated for a resorbable Mg-Dy based alloy. The initial hot-extruded condition is a fine-grained Resoloy® (Mg–Dy–Nd–Zn–Zr) alloy consisting of lamellar LPSO structures within the matrix. Solution heat treatment causes grain growth and the formation of blocky LPSO phases. The amount of the lamellar LPSO structures reduces. Quasi-static C-ring tests with and without Ringer solution were used to evaluate force–displacement curves and their fracture energy. The coarser-grained alloys tend to twin under plastic deformation, which is influencing the crack propagation. Blocky LPSO phases clearly hinder crack growth. The fine-grained extruded condition shows the highest force and displacement values to induce the crack, the solution heat-treated microstructure consisting of a good balance of grain size, matrix, and blocky LPSO phases and twins show highest fracture energy. Even if there might be an absorption of hydrogen, the ductility under stress corrosion is high.