Can Higgs inflation be saved with high-scale supersymmetry?

It is shown whether Higgs inflation can be saved as high-scale supersymmetry critically depends on the magnitude of the non-minimal coupling constant xi. For small xi <= 500, the threshold correction at scale M-P/xi is constrained with high precision. Its magnitude is in the narrow range of (-0.03, -0.02) and (-0.05, -0.04) for the wino and higgsino-singlino dark matter, respectively. In the large-xi region with xi >= 10(4), such high-scale supersymmetry is excluded by a too large threshold correction as required by Higgs inflation.