We report on an X-ray polarimetric observation of the high-mass X-ray binary LMC X-1 in the high/soft state, obtained by the Imaging X-ray Polarimetry Explorer (IXPE) in 2022 October. The measured polarization is below the minimum detectable polarization of 1.1 per cent (at the 99 per cent confidence level). Simultaneously, the source was observed with the Neutron Star Interior Composition Explorer (NICER), Nuclear Spectroscopic Telescope Array (NuSTAR), and Spectrum-Rontgen-Gamma (SRG)/Astronomical Roentgen Telescope – X-ray Concentrator (ART-XC) instruments, which enabled spectral decomposition into a dominant thermal component and a Comptonized one. The low 2–8 keV polarization of the source did not allow for strong constraints on the black hole spin and inclination of the accretion disc. However, if the orbital inclination of about 36◦ is assumed, then the upper limit is consistent with predictions for pure thermal emission from geometrically thin and optically thick discs. Assuming the polarization degree of the Comptonization component to be 0, 4, or 10 per cent, and oriented perpendicular to the polarization of the disc emission (in turn assumed to be perpendicular to the large-scale ionization cone orientation detected in the optical band), an upper limit to the polarization of the disc emission of 1.0, 0.9, or 0.9 per cent, respectively, is found (at the 99 per cent confidence level).