Carbon-based nanomaterials such as graphyne, graphene, and carbon nanotubes have attracted considerable attention for their applications, but questions remain regarding their biosafety through potential adverse interactions with important biomolecules. Here, we investigate the binding of a graphyne nanosheet and a graphyne quantum dot to calmodulin (CaM), a dynamic Ca2+ binding protein. Simulation results show that both the graphyne nanosheet and graphyne quantum dot are able to bind both Ca2+-bound and Ca2+-free CaM with similar binding affinities. From our simulations, graphyne quantum dots appear particularly worrisome for potential toxicity as they bind to and occlude the hydrophobic binding pocket of both Ca2+-bound and Ca2+-free CaM. In both the nanosheet and quantum dot systems, the binding interactions between graphyne and CaM are markedly hydrophobic and heavily suppress the Ca2+-free CaM dynamics. Our results reiterate that graphitic nanomaterials including graphyne may have negative impacts on both the structure and dynamics of key proteins such as CaM involved in calcium signal transduction.