Systematic 3D mapping of out-of-field doses induced by a therapeutic proton pencil scanning beam in a 300 × 300 × 600 mm3 water phantom was performed using a set of thermoluminescence detectors (TLDs): MTS-7 (7LiF:Mg,Ti), MTS-6 (6LiF:Mg,Ti), MTS-N (natLiF:Mg,Ti) and TLD-700 (7LiF:Mg,Ti), radiophotoluminescent (RPL) detectors GD-352M and GD-302M, and polyallyldiglycol carbonate (PADC)-based (C12H18O7) track-etched detectors. Neutron and gamma-ray doses, as well as linear energy transfer distributions, were experimentally determined at 200 points within the phantom. In parallel, the Geant4 Monte Carlo code was applied to calculate neutron and gamma radiation spectra at the position of each detector. For the cubic proton target volume of 100 × 100 × 100 mm3 (spread out Bragg peak with a modulation of 100 mm) the scattered photon doses along the main axis of the phantom perpendicular to the primary beam were approximately 0.5 mGy Gy-1 at a distance of 100 mm and 0.02 mGy Gy-1 at 300 mm from the center of the target. For the neutrons, the corresponding values of dose equivalent were found to be ~0.7 and ~0.06 mSv Gy-1, respectively. The measured neutron doses were comparable with the out-of-field neutron doses from a similar experiment with 20 MV x-rays, whereas photon doses for the scanning proton beam were up to three orders of magnitude lower.