The Scattering and Neutrino Detector at the LHC (SND@LHC) started taking data at the beginning of Run 3 of the LHC. The experiment is designed to perform measurements with neutrinos produced in proton-proton collisions at the LHC in an energy range between 100 GeV and 1 TeV. It covers a previously unexplored pseudo-rapidity range of 7.2<η<8.4. The detector is located 480 m downstream of the ATLAS interaction point in the TI18 tunnel. It comprises a veto system, a target consisting of tungsten plates interleaved with nuclear emulsion and scintillating fiber (SciFi) trackers, followed by a muon detector (UpStream, US and DownStream, DS). In this article we report the measurement of the muon flux in three subdetectors: the emulsion, the SciFi trackers and the DownStream Muon detector. The muon flux per integrated luminosity through an 18x18 cm(2 )area in the emulsion is: 1.5 ± 0.1(stat) x 10^4fb/cm^(2). The muon flux per integrated luminosity through a 31x31 cm^2 area in the centre of the SciFi is: 2.06 ± 0.01(stat) ± 0.12(sys) x 10^(4)fb/cm^(2) The muon flux per integrated luminosity through a 52x52 cm^2 area in the centre of the downstream muon system is: 2.35 ± 0.01(stat) ± 0.10(sys) x 10^(4)fb/cm^(2) The total relative uncertainty of the measurements by the electronic detectors is 6% for the SciFi and 4% for the DS measurement. The Monte Carlo simulation prediction of these fluxes is 20-25% lower than the measured values.