A search for the supersymmetric partners of quarks and gluons (squarks and gluinos) in final states containing hadronic jets and missing transverse momentum, but no electrons or muons, is presented. The data used in this search were recorded in 2015 and 2016 by the ATLAS experiment in $s$=13 TeV proton--proton collisions at the Large Hadron Collider, corresponding to an integrated luminosity of 36.1 fb$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$. The results are interpreted in the context of various models where squarks and gluinos are pair-produced and the neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 2.03 TeV for a simplified model incorporating only a gluino and the lightest neutralino, assuming the lightest neutralino is massless. For a simplified model involving the strong production of mass-degenerate first- and second-generation squarks, squark masses below 1.55 TeV are excluded if the lightest neutralino is massless. These limits substantially extend the region of supersymmetric parameter space previously excluded by searches with the ATLAS detector.