The SHiP experiment will search for very weakly interacting particles beyond the Standard Model which are produced in a 400 \GeV/$c$ proton beam dump at the CERN SPS. About $10^{11}$ muons per spill will be produced in the dump. To design the experiment such that the muon-induced background is minimized, a precise knowledge of the muon spectrum is required. To validate the muon flux generated by our Pythia and GEANT4 based Monte Carlo simulation (FairShip), we have measured the muon flux emanating from a SHiP-like target at the SPS. This target, consisting of 13 interaction lengths of slabs of molybdenum and tungsten, followed by a 2.4 m iron hadron absorber was placed in the H4 400~\GeV/$c$ proton beam line. To identify muons and to measure the momentum spectrum, a spectrometer instrumented with drift tubes and a muon tagger were used. During a three-week period a dataset for analysis corresponding to $(3.27\pm0.07)~\times~10^{11}$ protons on target was recorded. This amounts to approximatively 1\% of a SHiP spill.