The muon intensity and angular distribution in the shallow-underground laboratory Felsenkeller in Dresden, Germany have been studied using a portable muon detector based on the close cathode chamber design. Data has been taken at four positions in Felsenkeller tunnels VIII and IX, where a new 5 MV underground ion accelerator is being installed, and in addition at four positions in Felsenkeller tunnel IV, which hosts a low-radioactivity counting facility. At each of the eight positions studied, seven different orientations of the detector were used to compile a map of the upper hemisphere with 0.85{deg} angular resolution. The muon intensity is found to be suppressed by a factor of 40 due to the 45 m thick rock overburden, corresponding to 140 meters water equivalent. The angular data are matched by two different simulations taking into account the known geodetic features of the terrain: First, simply by determining the cutoff energy using the projected slant depth in rock and the known muon energy spectrum, and second, in a Geant4 simulation propagating the muons through a column of rock equal to the known slant depth. The present data are instrumental for studying muon-induced effects at these depths and also in the planning of an active veto for accelerator-based underground nuclear astrophysics experiments.