The first dedicated Z-boson mass measurement at the LHC with Z→μ^{+}μ^{-} decays is reported. The dataset uses proton-proton collisions at a center-of-mass energy of 13 TeV, recorded in 2016 by the LHCb experiment, and corresponds to an integrated luminosity of 1.7 fb^{-1}. A template fit to the μ^{+}μ^{-} mass distribution yields the following result for the Z-boson mass: m_{Z}=91,185.7±8.3±3.9 MeV, where the first uncertainty is statistical and the second systematic. This result is consistent with previous measurements and predictions from global electroweak fits.