We present the first measurements of the ratios of cross sections σ(pp¯→Z+c jet)/σ(pp¯→Z+jet) and σ(pp¯→Z+c jet)/σ(pp¯→Z+b jet) for the associated production of a Z boson with at least one charm or bottom quark jet. Jets have transverse momentum ​pjetT​>20  GeV and pseudorapidity |​ηjet​|<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 pp¯ collisions collected with the D0 detector at the Fermilab Tevatron Collider at s√=1.96  TeV. The measurements show significant deviations from perturbative QCD calculations and predictions from various event generators.