The growth of supermassive black holes and their host galaxies are thought to be linked, but the precise nature of this symbiotic relationship is still poorly understood. Both observations and simulations of galaxy formation suggest that the energy input from active galactic nuclei (AGNs), as the central supermassive black hole accretes material and grows, heats the interstellar material and suppresses star formation. In this Letter, we show that most host galaxies of moderate-luminosity supermassive black holes in the local universe have intermediate optical colors that imply the host galaxies are transitioning from star formation to quiescence, the first time this has been shown to be true for all AGNs independent of obscuration. The intermediate colors suggest that star formation in the host galaxies ceased roughly 100 Myr ago. This result indicates that either the AGNs are very long lived, accreting for more than 1 Gyr beyond the end of star formation, or there is a ~100 Myr time delay between the shutdown of star formation and detectable black hole growth. The first explanation is unlikely given current estimates for AGN lifetimes, so low-luminosity AGNs must shut down star formation before substantial black hole accretion activity is detected. The scarcity of AGN host galaxies in the blue cloud reported here challenges scenarios where significant star formation and black hole growth are coeval. Lastly, these observations also strongly support the "Unified Model" of AGNs as the host galaxy colors are independent of obscuration toward the central engine.