The incoming Imaging X-ray Polarimetry Explorer (IXPE) observations of X-ray binaries provide a new tool to investigate the underlying accretion geometry. Here, we report the first measurements of X-ray polarization of the extragalactic black-hole X-ray binary LMC X-3. We find a polarization fraction of $\sim 3~{{\ \rm per\ cent}}$ at a polarization angle of ~135° in the 2-8 keV energy band with statistical significance at the 7σ level. This polarization measurement significantly exceeds the minimum detectable polarization threshold of 1.2 per cent for the source, ascertained at a 99 per cent confidence level within the 2-8 keV energy band. The simultaneous spectro-polarimetric fitting of Neutron Star Interior Composition Explorer, Swift/X-Ray Telescope (XRT), and IXPE revealed the presence of a disc with a temperature of ~1 keV and a Comptonized component with a power-law index of ~2.4, confirming the soft nature of the source. The polarization degree increases with energy from ~3 per cent in the 2-5.7 keV band to ~9 per cent in the 5.7-8 keV band, while the polarization angle is energy independent. The observed energy dependence and the sudden jump of polarization fraction above 5 keV supports the idea of a static slab coronal geometry for the Comptonizing medium of LMC X-3.