Dark matter with Planck-scale mass (?1019 GeV/c2) 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 8.3×106 and 1.2×1019 GeV/c2, and Ar40-scattering cross sections between 1.0×10-23 and 2.4×10-18 cm2. These results are interpreted as constraints on composite dark matter models with two different nucleon-to-nuclear cross section scalings