Graphene oxide (GO) and functionalized carbon nanotubes (f-CNTs) (each in the concentration range of 0.01–1.00 wt/wt%) were investigated as the reinforcing agent in a poly(methyl methacrylate) (PMMA)/hydroxyapatite (HA) bone cement. Mixed results were obtained for the changes in the mechanical properties determined (storage modulus, bending strength, and elastic modulus) for the reinforced cement relative to the unreinforced counterpart; that is, some property changes were increased while others were decreased. We postulate that this outcome is a consequence of the fact that each of the nanofillers hampered the polymerization process in the cement; specifically, the nanofiller acts as a scavenger of the radicals produced during polymerization reaction due to the delocalized π-bonds. Results obtained from the chemical structure and polymer chain size distribution determined, respectively, by nuclear magnetic resonance and size exclusion chromatography analysis, on the polymer extracted from the specimens support the postulated mechanism. Furthermore, in the case of the 0.5 wt/wt% GO-reinforced cement, we showed that when the concentration of the radical species in the PMMA bone cement was doubled, mechanical properties markedly improved (relative to the value in the unreinforced cement), suggesting suppression of the aforementioned scavenger activity.