  A precision measurement of the $Z$ boson production cross-section at
$\sqrt{s} = 13$ TeV in the forward region is presented, using $pp$ collision
data collected by the LHCb detector, corresponding to an integrated luminosity
of 5.1 fb$^{-1}$. The production cross-section is measured using
$Z\rightarrow\mu^+\mu^-$ events within the fiducial region defined as
pseudorapidity $2.0<\eta<4.5$ and transverse momentum $p_{T}>20$ GeV/$c$ for
both muons and dimuon invariant mass $60<M_{\mu\mu}<120$ GeV/$c^2$. The
integrated cross-section is determined to be \begin{equation*}
\sigma(Z\rightarrow\mu^+\mu^-) = 196.4 \pm 0.2 \pm 1.6 \pm 3.9~pb,
\end{equation*} where the first uncertainty is statistical, the second is
systematic, and the third is due to the luminosity determination. The measured
results are in agreement with theoretical predictions within uncertainties.
