Measuring the Higgs couplings accurately at colliders is one of the best routes for finding physics Beyond the Standard Model (BSM). If the measured couplings deviate from the SM predictions, then this would give rise to energy-growing processes that violate tree-level unitarity at some energy scale, indicating new physics. In this paper, we extend previous work on unitarity bounds from the Higgs potential and the Higgs couplings to vector bosons, the top quark, γγ and γZ; to the Higgs coupling to gg. We show that the scale of new physics could be as low as ∼10 TeV, which although beyond the reach of the LHC, is well within the reach of the future 100-TeV collider, and can also be probed indirectly in the High Luminosity LHC (HL-LHC).