We present a complete next-to-leading order calculation for the total cross section for inclusive Higgs pair production via bottom-quark fusion at the CERN Large Hadron Collider in the minimal supersymmetric standard model and the minimal supergravity model. We emphasize the contributions of squark and gluino loops and the decoupling properties of our results for heavy squark and gluino masses. The enhanced couplings of the $b$ quark to the Higgs bosons in supersymmetric models with large $\mathrm{tan}\ensuremath{\beta}$ yield large next-to-leading order supersymmetry QCD corrections in some regions of parameter space.