We present the first measurements of the ratios of cross sections, \sigma(ppbar -> Z+c jet)/\sigma(ppbar -> Z+jet) and \sigma(ppbar -> Z+c jet)/\sigma(ppbar -> Z+b jet) for the associated production of a Z boson with at least one charm or bottom quark jet. Jets have transverse momentum p_{T}>20 GeV and pseudorapidity |\eta|<2.5. These cross section ratios are measured differentially as a function of jet and $Z$ boson transverse momenta, based on 9.7 fb^{-1} of ppbar collisions collected with the D0 detector at the Fermilab Tevatron Collider at sqrt(s) = 1.96 TeV. The measurements show significant deviations from perturbative QCD calculations and predictions from various event generators.