The hypothesis that high-Curie-temperature ferromagnetism in cobalt-doped ZnO (Co2+:  ZnO) is mediated by charge carriers was tested by controlled introduction and removal of the shallow donor interstitial zinc. Using oriented epitaxial Co2+:  ZnO films grown by chemical vapor deposition, kinetics measurements demonstrate a direct correlation between the oxidative quenching of ferromagnetism and the diffusion and oxidation of interstitial zinc. These results demonstrate controlled systematic variation of a key parameter involved in the ferromagnetism of Co2+:  ZnO and, in the process, unambiguously reveal this ferromagnetism to be dependent upon charge carriers. The distinction between defect-bound and free carriers in Co2+:  ZnO is discussed.