A search for heavy long-lived multicharged particles is performed using the ATLAS detector at the LHC. Data with an integrated luminosity of $36.1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected in 2015 and 2016 from proton-proton collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ are examined. Particles producing anomalously high ionization, consistent with long-lived massive particles with electric charges from $|q|=2e$ to $|q|=7e$, are searched for. No events are observed, and 95% confidence level cross-section upper limits are interpreted as lower mass limits for a Drell-Yan production model. Multicharged particles with masses between 50 and 980--1220 GeV (depending on their electric charge) are excluded.