The lattice thermal conductivity (κ) of the thermoelectric materials, Mg2Si, Mg2Sn, and their alloys, are calculated for bulk and nanowires, without adjustable parameters. We find good agreement with bulk experimental results. For large nanowire diameters, size effects are stronger for the alloy than for the pure compounds. For example, in 200 nm diameter nanowires κ is lower than its bulk value by 30%, 20%, and 20% for Mg2Si0.6Sn0.4, Mg2Si, and Mg2Sn, respectively. For nanowires less than 20 nm thick, the relative decrease surpasses 50%, and it becomes larger in the pure compounds than in the alloy. At room temperature, κ of Mg2Si_{x}Sn_{1−x} is less sensitive to nanostructuring size effects than Si_{x}Ge_{1−x}, but more sensitive than PbTe_{x}Se_{1−x}. This suggests that further improvement of Mg2Si_{x}Sn_{1−x} as a nontoxic thermoelectric may be possible.