We have compiled a sample of 26 metal-poor galaxies with 12 + log(O/H) < 8.1 with both infrared continuum and 1.4 GHz radio continuum data. By comparing to galaxies at higher metallicity, we have investigated the IR-radio relationship's dependence on metallicity at the 24, 70, 100, and 160 m bands, as well as the integrated FIR luminosity. It is found that metal-poor galaxies have on average lower than metal-rich ones, with larger offsets at longer IR wavelengths, from −0.06 dex in to −0.6 dex in . The of all galaxies as a whole at 160 m show positive trends with the metallicity and IR-to-FUV ratio and negative trends with the IR color, while those at lower IR wavelengths show weaker correlations. We propose a mechanism that invokes the combined effects of low obscured-SFR-to-total-SFR fraction and warm dust temperature at low metallicity to interpret the above behavior of , with the former reducing the IR radiation and the latter further reducing the IR emission at longer IR wavelengths. Other mechanisms that are related to the radio emission, including the enhanced magnetic field strength and increased thermal radio contribution, are unable to reconcile the IR-wavelength-dependent differences of between metal-poor and metal-rich galaxies. In contrast to , the mean total-SFR-to-radio ratio of metal-poor galaxies is the same as that for metal-rich galaxies, indicating the 1.4 GHz radio emission is still an effective tracer of SFRs at low metallicity.