Several N-heterocyclic carbenes (NHCs) are experimentally observed upon the addition of muonium (Mu), and the hyperfine coupling constants (HFCCs) of muon are measured. Theoretical investigation of Mu has been challenging due to significant quantum effects. Herein, we performed an ab initio path integral molecular dynamics (PIMD) simulation, which accurately considers multi-dimensional quantum effects, to theoretically investigate muoniated 1,3-dihydro-2H-imidazole-2-ylidene (Mu-IY). Our findings indicate that quantum effects have two contradictory contributions: the quantum effect of bond vibrations increases the HFCC values, whereas that of out-of-plane angular vibrations decreases the HFCC values. Moreover, we show that the HFCC values of other NHCs can be predicted without the PIMD simulations by applying the structural changes caused by the quantum effect derived from the PIMD simulations of Mu-IY.