We present a search for the rare flavor-changing neutral-current decay B0→K∗0τ+τ- with data collected by the Belle II experiment at the SuperKEKB electron-positron collider. The analysis uses a 365 fb-1 data sample recorded at the center-of-mass energy of the Υ(4S) resonance. One of the B mesons produced in the Υ(4S)→B0B ̄0 process is fully reconstructed in a hadronic decay mode, while its companion B meson is required to decay into a K∗0 and two τ leptons of opposite charge. The τ leptons are reconstructed in final states with a single electron, muon, charged pion or charged ρ meson, and additional neutrinos. We set an upper limit on the branching fraction of B(B0→K∗0τ+τ-)<1.8×10-3 at the 90% confidence level, which is the most stringent constraint reported to date.