Nanomaterials exhibiting plasmonic optical responses are impacting sensing, information processing, catalysis, solar, and photonics technologies. Recent advances have expanded the portfolio of plasmonic nanostructures into doped semiconductor nanocrystals, which allow dynamic manipulation of carrier densities. Once interpreted as intraband single-electron transitions, the infrared absorption of doped semiconductor nanocrystals is now commonly attributed to localized surface plasmon resonances and analyzed using the classical Drude model to determine carrier densities. Here, we show that the experimental plasmon resonance energies of photodoped ZnO nanocrystals with controlled sizes and carrier densities diverge from classical Drude model predictions at small sizes, revealing quantum plasmons in these nanocrystals. A Lorentz oscillator model more adequately describes the data and illustrates a closer link between plasmon resonances and single-electron transitions in semiconductors than in metals, highlighting a fundamental contrast between these two classes of plasmonic materials.