The production of jets in association with Z bosons, reconstructed via the μ^{+}μ^{-} and e^{+}e^{-} decay channels, is studied in pp and, for the first time, in Pb-Pb collisions. Both data samples were collected by the CMS experiment at the LHC, at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The Pb-Pb collisions were analyzed in the 0%-30% centrality range. The back-to-back azimuthal alignment was studied in both pp and Pb-Pb collisions for Z bosons with transverse momentum p_{T}^{Z}>60 GeV/c and a recoiling jet with p_{T}^{jet}>30 GeV/c. The p_{T} imbalance x_{jZ}=p_{T}^{jet}/p_{T}^{Z}, as well as the average number of jet partners per Z, R_{jZ}, was studied in intervals of p_{T}^{Z}. The R_{jZ} is found to be smaller in Pb-Pb than in pp collisions, which suggests that in Pb-Pb collisions a larger fraction of partons associated with the Z bosons fall below the 30 GeV/c p_{T}^{jet} threshold because they lose energy.