Ratios of cross sections, (\sigma \left(Z+c\text{}\text{}\text{jets}\right)/\sigma \left(Z+\text{jets}\right)), (\sigma \left(Z+b\text{}\text{}\text{jets}\right)/\sigma \left(Z+\text{jets}\right)), and (\sigma \left(Z+c\text{}\text{}\text{jets}\right)/\phantom{\rule{0ex}{0ex}}\sigma \left(Z+b\text{}\text{}\text{jets}\right)) in the associated production of a (Z) boson with at least one charm or bottom quark jet are measured in proton-proton collisions at (\sqrt{s}=13\text{}\text{}\mathrm{TeV}). The data sample, collected by the CMS experiment at the CERN LHC, corresponds to an integrated luminosity of (35.9\text{}\text{}{\mathrm{fb}}^{-1}), with a fiducial volume of ({p}{T}>30\text{}\text{}\mathrm{GeV}) and (|\eta |<2.4) for the jets, where ({p}{T}) and (\eta ) represent transverse momentum and pseudorapidity, respectively. The (Z) boson candidates come from leptonic decays into electrons or muons with ({p}{T}>25\text{}\text{}\mathrm{GeV}) and (|\eta |<2.4), and the dilepton mass satisfies (71<{m}{Z}<111\text{}\text{}\mathrm{GeV}). The measured values are (\sigma \left(Z+c\text{}\text{}\text{jets}\right)/\sigma \left(Z+\text{jets}\right)=0.102±0.002±0.009), (\sigma \left(Z+b\text{}\text{}\text{jets}\right)/\sigma \left(Z+\text{jets}\right)=\phantom{\rule{0ex}{0ex}}0.0633±0.0004±0.0015), and (\sigma \left(Z+c\text{}\text{}\text{jets}\right)/\sigma \left(Z+b\text{}\text{}\text{jets}\right)=1.62±0.03±0.15). Results on the inclusive and differential cross section ratios as functions of jet and (Z) boson transverse momentum are compared with predictions from leading and next-to-leading order perturbative quantum chromodynamics calculations. These are the first measurements of the cross section ratios at 13 TeV.