The process e$^+$e$^- \rightarrow$~e$^+$e$^-$Z$/\gamma^*$ is studied with the OPAL detector at LEP at a centre of mass energy of $\sqrt{s} = 189$~GeV. The cross-section times the branching ratio of the Z/$\gamma^*$ decaying into hadrons is measured within Lorentz invariant kinematic limits to be $(1.2 \pm 0.3 \pm 0.1)$~pb for invariant masses of the hadronic system between $5$~GeV and $60$~GeV and $(0.7 \pm 0.2 \pm 0.1)$~pb for hadronic masses above 60~GeV. The differential cross-sections of the Mandelstam variables $\hat{s}$, $\hat{t}$, and $\hat{u}$ 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 e$\gamma \rightarrow$~eZ/$\gamma^*$ are derived.