Vector bosons, such as dark photon A′ or Z′, can couple to muons and be produced in the bremsstrahlung reaction μ− + N → μ− + N + A′ (Z′). Their possible subsequent invisible decay can be detected in fixed target experiments through missing energy/momentum signature. In such experiments, not only is the energy transfer to A ′(Z′) important but also the recoil muon angle ψμ′. In this paper, we derive the total and the double differential cross sections involved in this process using the phase space Weizsäcker-Williams and improved Weizsäcker-Williams approximations, as well as using exact-tree-level calculations. As an example, we compare the derived cross sections and resulting signal yields in the NA 64μ experiment that uses a 160 GeV muon beam at the CERN Super Proton Synchrotron accelerator. We also discuss its impact on the NA 64μ expected sensitivity to explore the (g−2)μ anomaly favored region with a Z′ boson considering 1012 muons accumulated on target.