We present the first search for a dark matter annual modulation signal in the Southern Hemisphere conducted with NaI(Tl) detectors, performed by the DM-Ice17 experiment. Nuclear recoils from dark matter interactions are expected to yield an annually modulated signal independent of location within the Earths hemispheres. DM-Ice17, the first step in the DM-Ice experimental program, consists of 17 kg of NaI(Tl) located at the South Pole under 2200 m.w.e. overburden of Antarctic glacial ice. Taken over 3.6 years for a total exposure of 60.8 kg yr, DM-Ice17 data are consistent with no modulation in the energy range of 4-20 keV, providing the strongest limits on weakly interacting massive particle dark matter from a direct detection experiment located in the Southern Hemisphere. The successful deployment and stable long-term operation of DM-Ice17 establishes the South Pole ice as a viable location for future dark matter searches and in particular for a high-sensitivity NaI(Tl) dark matter experiment to directly test the DAMA/LIBRA claim of the observation of dark matter.