© 2019 Many Galactic sources of gamma rays, such as supernova remnants, are expected to produce neutrinos with a typical energy cutoff well below 100 TeV. For the IceCube Neutrino Observatory located at the South Pole, the southern sky, containing the inner part of the Galactic plane and the Galactic Center, is a particularly challenging region at these energies, because of the large background of atmospheric muons. In this paper, we present recent advancements in data selection strategies for track-like muon neutrino events with energies below 100 TeV from the southern sky. The strategies utilize the outer detector regions as veto and features of the signal pattern to reduce the background of atmospheric muons to a level which, for the first time, allows IceCube searching for point-like sources of neutrinos in the southern sky at energies between 100 GeV and several TeV in the muon neutrino charged current channel. No significant clustering of neutrinos above background expectation was observed in four years of data recorded with the completed IceCube detector. Upper limits on the neutrino flux for a number of spectral hypotheses are reported for a list of astrophysical objects in the southern hemisphere.