The process e+e− → e+e−Z/γ∗ is studied with the OPAL detector at LEP at a centre of mass energy of √s = 189 GeV. The cross-section times the branching ratio of the Z/γ∗ decaying into hadrons is measured within Lorentz invariant kinematic limits to be (1.2 ± 0.3 ± 0.1) pb for invariant masses of the hadronic system between 5 GeV and 60 GeV and (0.7 ± 0.2 ± 0.1) pb for hadronic masses above 60 GeV. The differential cross-sections of the Mandelstam variables ˆs, ˆt, and ˆu are measured and compared with the predictions from the Monte Carlo generators grc4f and PYTHIA. From this, based on a factorisation ansatz, the total and differential cross-sections for the subprocess eγ → eZ/γ∗ are derived.