At the earliest epochs of structure formation in cold dark matter (CDM) cosmologies, the smallest nonlinear objects are the numerous small halos that condense with virial temperatures below 10,000 K. Such "minihalos" are not yet resolved in large-scale three-dimensional cosmological simulations. Here we employ a semi-analytic method, combined with three-dimensional simulations of individual minihalos, to examine their importance during cosmological reionization. We show that, depending on when

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... eionization takes place, they potentially play an important role as sinks of ionizing radiation. If reionization occurs at sufficiently high redshifts (z_r > 20), the intergalactic medium is heated to 10,000 K and most minihalos never form. On the other hand, if z_r < 20, a significant fraction (>10 percent) of all baryons have already collapsed into minihalos, and are subsequently removed from the halos by photoevaporation as the ionizing background flux builds up. We show that this process can require a significant budget of ionizing photons; exceeding the production by a straightforward extrapolation back in time of known quasar and galaxy populations by a factor of up to 10 and 3, respectively.