  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 $J/\psi \rightarrow
\gamma+\textrm{invisible}$
