We determine Λ_MS^(n_f=2) by fitting perturbative expressions for the quark-antiquark static potential to lattice results for QCD with n_f = 2 dynamical quark flavors. To this end we use the perturbative static potential at the presently best known accuracy, i.e. up to O(α_s⁴), in momentum space. The lattice potential is computed on a fine lattice with a = 0.042 fm in position space. To allow for a comparison and matching of both results, the lattice potential is transformed into momentum space by means of a discrete Fourier transform. The value of Λ_MS^(n_f=2) is extracted in momentum space. All sources of statistical and systematic errors are discussed. The uncertainty in the value of Λ_MS^(n_f=2) is found to be smaller than that obtained in a recent position space analysis of the static potential based on the same lattice data. Our final results are r₀ Λ_MS^(n_f=2)=0.692(31) and Λ_MS^(n_f=2)=331(21) MeV.