A search for T and Y vector-like quarks produced in proton-proton collisions at a centre-of-mass energy of 13 TeV and decaying into Wb in the fully hadronic final state is presented. The search uses 139 fb$^{−1}$ of data collected by the ATLAS detector at the LHC from 2015 to 2018. The final state is characterised by a hadronically decaying W boson with large Lorentz boost and a b-tagged jet, which are used to reconstruct the invariant mass of the vector-like quark candidate. The main background is QCD multijet production, which is estimated using a data-driven method. Upon finding no significant excess in data, mass limits at 95% confidence level are obtained as a function of the global coupling parameter, κ. The observed lower limits on the masses of Y quarks with κ = 0.5 and κ = 0.7 are 2.0 TeV and 2.4 TeV, respectively. For T quarks, the observed mass limits are 1.4 TeV for κ = 0.5 and 1.9 TeV for κ = 0.7.[graphic not available: see fulltext]