A search for supersymmetry in events with large missing transverse momentum, jets, and at least one hadronically decaying τ-lepton is presented. Two exclusive final states with either exactly one or at least two τ-leptons are considered. The analysis is based on proton-proton collisions at s=13 TeV corresponding to an integrated luminosity of 36.1 fb-1 delivered by the Large Hadron Collider and recorded by the ATLAS detector in 2015 and 2016. No significant excess is observed over the Standard Model expectation. At 95% confidence level, model-independent upper limits on the cross section are set and exclusion limits are provided for two signal scenarios: a simplified model of gluino pair production with τ-rich cascade decays, and a model with gauge-mediated supersymmetry breaking (GMSB). In the simplified model, gluino masses up to 2000 GeV are excluded for low values of the mass of the lightest supersymmetric particle (LSP), while LSP masses up to 1000 GeV are excluded for gluino masses around 1400 GeV. In the GMSB model, values of the supersymmetry-breaking scale are excluded below 110 TeV for all values of tanβ in the range 2≤tanβ≤60, and below 120 TeV for tanβ>30.