Despite the importance of feedback from active galactic nuclei (AGNs) in models of galaxy evolution, observational constraints on the influence of AGN feedback on star formation remain weak. To this end, we have compared the star formation trends of 279 low-redshift AGN galaxies with 558 inactive control galaxies using integral field unit spectroscopy from the Sloan Digital Sky Survey-IV Mapping Nearby Galaxies at Apache Point Observatory survey. With a Gaussian-process-based methodology, we reconstruct nonparametric star formation histories in spatially resolved spaxels covering the face of each galaxy. Based on the galaxy-wide star formation rates (SFRs) alone, we find no obvious signatures of AGN feedback. However, the AGN galaxies have significantly suppressed central (kiloparsec-scale) SFRs, lying up to a factor of 2 below those of the control galaxies, providing direct observational evidence of AGN feedback suppressing star formation. The suppression of central SFRs in the AGN galaxies began in the central regions ∼6 Gyr ago (redshift z ∼ 0.7), taking place over a few gigayears. A small subset of the AGN galaxies were rapidly driven to quiescence shortly before being observed (in the last 500 Myr), potentially indicating instances of AGN-driven feedback. More frequently, however, star formation continues in the AGN galaxies, with suppression primarily in the central regions. This is suggestive of a picture in which integrated (gigayear-timescale) AGN feedback can significantly affect central star formation, but may be inefficient in driving galaxy-wide quenching in low-redshift galaxies, instead leaving them in the green valley.