An experimental study of the production of up-going charged particles in inelastic interactions of down-going underground muons is reported, using data obtained from the MACRO detector at the Gran Sasso Laboratory. In a sample of 12.2 x 106 single muons, corresponding to a detector lifetime of 1.55y, 243 events are observed having an up-going particle associated with a down-going muon. These events are analysed to determine the range and emission angle distributions of the up-going particle, corrected for detection and reconstruction efficiency. Measurements of the muon neutrino flux by underground detectors are often based on the observation of through-going and stopping muons produced in νμ interactions in the rock below the detector. Up-going particles produced by an undetected down-going muon are a potential background source in these measurements. The implications of this background for neutrino studies using MACRO are discussed.