The first study of the angular distribution of μ^{+}μ^{-} pairs produced in the forward rapidity region via the Drell-Yan reaction pp→γ^{*}/Z+X→ℓ^{+}ℓ^{-}+X is presented, using data collected with the LHCb detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.1 fb^{-1}. The coefficients of the five leading terms in the angular distribution are determined as a function of the dimuon transverse momentum and rapidity. The results are compared to various theoretical predictions of the Z-boson production mechanism and can also be used to probe transverse-momentum-dependent parton distributions within the proton.