A search is performed for a new sub-GeV vector boson () mediated production of dark matter () in the fixed-target experiment, NA64, at the CERN SPS. The , called dark photon, can be generated in the reaction of 100 GeV electrons dumped against an active target followed by its prompt invisible decay . The experimental signature of this process would be an event with an isolated electron and large missing energy in the detector. From the analysis of the data sample collected in 2016 corresponding to electrons on target no evidence of such a process has been found. New stringent constraints on the mixing strength with photons, , for the mass range are derived. For models considering scalar and fermionic thermal dark matter interacting with the visible sector through the vector portal the 90% C.L. limits on the dark-matter parameter are obtained for the dark coupling constant and dark-matter masses . The lower limits for pseudo-Dirac dark matter in the mass region are more stringent than the corresponding bounds from beam dump experiments. The results are obtained by using exact tree level calculations of the production cross sections, which turn out to be significantly smaller compared to the one obtained in the Weizsäcker-Williams approximation for the mass region .