(1) Background: sewage sludge is a by-product of wastewater treatment, which needs to be managed appropriately, e.g., in composting processes. The application of municipal sewage sludge composts (MSSCs) as a soil amendment is a potential way to effectively manage sewage sludge. (2) Methods: this paper presents the results of a vegetation pot experiment undertaken to assess the suitability of Dactylis glomerata L. and MSSC in the aided phytostabilization technique when applied on soils from an area effected by industrial pressure; this is characterized by high levels of heavy metal (HM). The contents of HMs in the test plant (the roots and above-ground parts), as well as in the soil and MSSC, were determined via an atomic spectrometry method. (3) Results: the application of MSSC positively contributed to an increased production of plant biomass and an increase in the pH in the soil. Concentrations of Cu, Cd, Pb, Zn, and Cr were higher in the roots than in the above-ground parts of Dactylis glomerata L. The addition of MSSC contributed most significantly to the considerable reduction in Ni, Pb, and Zn contents in the soil after the experiment. (4) Conclusions: MSSC can support the phytostabilization of soils contaminated with high levels of HMs.