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A search for standard model Higgs bosons (H) produced with transverse momentum (pT) greater than 450 GeV and decaying to bottom quark-antiquark pairs (bb¯¯¯bb¯) is performed using proton-proton collision data collected by the CMS experiment at the LHC at √s = 13 TeV. The data sample corresponds to an integrated luminosity of 137 fb−1. The search is inclusive in the Higgs boson production mode. Highly Lorentz-boosted Higgs bosons decaying to bb¯¯¯bb¯ are reconstructed as single large-radius jets, and are identified using jet substructure and a dedicated b tagging technique based on a deep neural network. The method is validated with Z → bb¯¯¯bb¯ decays. For a Higgs boson mass of 125 GeV, an excess of events above the background assuming no Higgs boson production is observed with a local significance of 2.5 standard deviations (σ), while the expectation is 0.7. The corresponding signal strength and local significance with respect to the standard model expectation are μH = 3.7 ± 1.2(stat)+0.8−0.7−0.7+0.8(syst)+0.8−0.5−0.5+0.8(theo) and 1.9 σ. Additionally, an unfolded differential cross section as a function of Higgs boson pT for the gluon fusion production mode is presented, assuming the other production modes occur at the expected rates.