Dark matter with Planck-scale mass (≃10^{19} GeV/c^{2}) arises in well-motivated theories and could be produced by several cosmological mechanisms. A search for multiscatter signals from supermassive dark matter was performed with a blind analysis of data collected over a 813 d live time with DEAP-3600, a 3.3 t single-phase liquid argon-based detector at SNOLAB. No candidate signals were observed, leading to the first direct detection constraints on Planck-scale mass dark matter. Leading limits constrain dark matter masses between 8.3×10^{6} and 1.2×10^{19} GeV/c^{2}, and ^{40}Ar-scattering cross sections between 1.0×10^{-23} and 2.4×10^{-18} cm^{2}. These results are interpreted as constraints on composite dark matter models with two different nucleon-to-nuclear cross section scalings.