We study the gas phase metallicity (O/H) and nitrogen abundance gradients traced by star-forming regions in a representative sample of 550 nearby galaxies in the stellar mass range 109–1011.5 M⊙ with resolved spectroscopic data from the Sloan Digital Sky Survey IV Mapping Nearby Galaxies at Apache Point Observatory survey. Using strong-line ratio diagnostics (R23 and O3N2 for metallicity and N2O2 for N/O) and referencing to the effective (half-light) radius (Re), we find that the metallicity gradient steepens with stellar mass, lying roughly flat among galaxies with log (M⋆/M⊙) = 9.0 but exhibiting slopes as steep as −0.14 dex R−1eRe−1 at log (M⋆/M⊙) = 10.5 (using R23, but equivalent results are obtained using O3N2). At higher masses, these slopes remain typical in the outer regions of our sample (R > 1.5Re), but a flattening is observed in the central regions (R < 1Re). In the outer regions (R > 2.0Re), we detect a mild flattening of the metallicity gradient in stacked profiles, although with low significance. The N/O ratio gradient provides complementary constraints on the average chemical enrichment history. Unlike the oxygen abundance, the average N/O profiles do not flatten out in the central regions of massive galaxies. The metallicity and N/O profiles both depart significantly from an exponential form, suggesting a disconnect between chemical enrichment and stellar mass surface density on local scales. In the context of inside-out growth of discs, our findings suggest that central regions of massive galaxies today have evolved to an equilibrium metallicity, while the nitrogen abundance continues to increase as a consequence of delayed secondary nucleosynthetic production.