Abstract: A search for a new Z′ gauge boson associated with (un)broken B−L symmetry in the keV–GeV mass range is carried out for the first time using the missing-energy technique in the NA64 experiment at the CERN SPS. From the analysis of the data with 3.22×10^11 electrons on target collected during 2016–2021 runs, no signal events were found. This allows us to derive new constraints on the Z′−e coupling strength, which, for the mass range 0.3≲ mZ′≲ 100  MeV, are more stringent compared to those obtained from the neutrino-electron scattering data.