The nature of multipolar order and hyperfine-enhanced (HE) $^{141}$Pr nuclear spin dynamics in PrV$_2$Al$_{20}$ was investigated using the muon spin relaxation technique. No explicit sign of time-reversal symmetry breaking was found below the multipolar order temperature $T_Qsim 0.6$ K in a zero applied field as anticipated on the basis of the antiferroquadrupolar (AFQ) order picture proposed by Sakai and Nakatsuji [J. Phys. Soc. Jpn. 80, 063701 (2011)]. Further evidence of the nonmagnetic ground state was obtained from the observation of HE $^{141}$Pr nuclear spin fluctuations in the MHz scale. A marked increase in the muon spin-lattice relaxation rate (1/$T_{rm 1,mu}$) was observed below 1 K with decreasing temperature, which was attributed to the perturbation on the HE $^{141}$Pr nuclear spin dynamics associated with the development of AFQ correlations. The longitudinal field dependence of 1/$T_{rm 1,mu}$ revealed that the enhanced $^{141}$Pr nuclear spin accidentally has an effective gyromagnetic ratio close to that of the muon.
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