We study the shape of the gas-phase mass-metallicity relation ( MZR ) of a combined sample of present-day dwarf and high-mass star-forming galaxies using IZI , a Bayesian formalism for measuring chemical abundances presented in Blanc et al . ( 2015 ) . We observe a characteristic stellar mass scale at M _ { * } \simeq 10 ^ { 9.5 } M _ { \odot } , above which the ISM undergoes a sharp increase in its level of chemical enrichment . In the 10 ^ { 6 } -10 ^ { 9.5 } M _ { \odot } range the MZR follows a shallow power-law ( Z \propto M ^ { \alpha } _ { * } ) with slope \alpha = 0.14 \pm 0.08 . At approaching M _ { * } \simeq 10 ^ { 9.5 } M _ { \odot } the MZR steepens significantly , showing a slope of \alpha = 0.37 \pm 0.08 in the 10 ^ { 9.5 } -10 ^ { 10.5 } M _ { \odot } range , and a flattening towards a constant metallicity at higher stellar masses . This behavior is qualitatively different from results in the literature that show a single power-law MZR towards the low mass end . We thoroughly explore systematic uncertainties in our measurement , and show that the shape of the MZR is not induced by sample selection , aperture effects , a changing N/O abundance , the adopted methodology to construct the MZR , secondary dependencies on star formation activity , nor diffuse ionized gas ( DIG ) contamination , but rather on differences in the method used to measure abundances . High resolution hydrodynamical simulations of galaxies can qualitatively reproduce our result , and suggest a transition in the ability of galaxies to retain their metals for stellar masses above this threshold . The MZR characteristic mass scale also coincides with a transition in the scale height and clumpiness of cold gas disks , and a typical gas fraction below which the efficiency of star formation feedback for driving outflows is expected to decrease sharply .