We measure the branching fraction of the decay B0→J/ψω using data collected with the Belle II detector at the SuperKEKB collider. The data contain (387±6)×106 BB ̄ meson pairs produced in energy-asymmetric e+e- collisions at the δ(4S) resonance. The measured branching fraction B(B0→J/ψω)=(2.16±0.30±0.14)×10-5, where the first uncertainty is statistical and the second is systematic, is more precise than previous results and constitutes the first observation of the decay with a significance of 6.5 standard deviations.