  We report on a direct search for sub-GeV dark photons (A') which might be
produced in the reaction e^- Z \to e^- Z A' via kinetic mixing with photons by
100 GeV electrons incident on an active target in the NA64 experiment at the
CERN SPS. The A's would decay invisibly into dark matter particles resulting in
events with large missing energy. No evidence for such decays was found with
2.75\cdot 10^{9} electrons on target. We set new limits on the \gamma-A' mixing
strength and exclude the invisible A' with a mass < 100 MeV as an explanation
of the muon g_\mu-2 anomaly.
