This Letter presents direct searches for lepton flavour violation in Higgs boson decays, $H\to e\tau$ and $H\to \mu \tau$, performed with the ATLAS detector at the LHC. The searches are based on a data sample of proton-proton collisions at a centre-of-mass energy $s=13$ TeV, corresponding to an integrated luminosity of $36.1\mathrm{fb}-1$. No significant excess is observed above the expected background from Standard Model processes. The observed (median expected) 95 % confidence-level upper limits on the lepton-flavour-violating branching ratios are $0.47\%$ ($0.34-0.10+0.13\%$) and $0.28\%$ ($0.37-0.10+0.14\%$) for $H\to e\tau$ and $H\to \mu \tau$, respectively.