Measurements of differential cross sections are presented for the production of a Z boson and at least one hadronic jet in proton-proton collisions at root s = 7 TeV, recorded by the CMS detector, using a data sample corresponding to an integrated luminosity of 4.9 fb(-1). The jet multiplicity distribution is measured for up to six jets. The differential cross sections are measured as a function of jet transverse momentum and pseudorapidity for the four highest transverse momentum jets. The distribution of the scalar sum of jet transverse momenta is also measured as a function of the jet multiplicity. The measurements are compared with theoretical predictions at leading and next-to-leading order in perturbative QCD.