In this work, we present the first lattice QCD study on the invisible decay $J/\psi \rightarrow \gamma\nu\bar{\nu}$. The calculation is accomplished using $N_f=2$ twisted mass fermion ensembles. The excited-state effects are observed and eliminated using a multi-state fit. The impact of finite-volume effects is also examined and confirmed to be well-controlled. After a continuous extrapolation under three lattice spacings, we obtain the branching fraction as $\operatorname{Br}[J/\psi \rightarrow \gamma\nu\bar{\nu}]=1.00(9)(7)\times 10^{-10}$, where the first error is the statistical error and the second is an estimate of the systematics. The exact theoretical prediction can be used to remove the only invisible contamination from the standard model background in searching for the possible dark matter by the channel $J/\psi \rightarrow \gamma+\textrm{invisible}$.