  This paper reports constraints on Higgs boson production with transverse
momentum above 1 TeV. The analyzed data from proton-proton collisions at a
center-of-mass energy of 13 TeV were recorded with the ATLAS detector at the
Large Hadron Collider from 2015 to 2018 and correspond to an integrated
luminosity of 136 fb$^{-1}$. Higgs bosons decaying into $b\bar{b}$ are
reconstructed as single large-radius jets recoiling against a hadronic system
and identified by the experimental signature of two $b$-hadron decays. The
experimental techniques are validated in the same kinematic regime using the
$Z\rightarrow b\bar{b}$ process.The 95$\% $ confidence-level upper limit on the
cross section for Higgs boson production with transverse momentum above 450 GeV
is 115 fb, and above 1 TeV it is 9.6 fb. The Standard Model cross section
predictions for a Higgs boson with a mass of 125 GeV in the same kinematic
regions are 18.4 fb and 0.13 fb, respectively.
