Likelihood-based algorithms identify the modulation of the transmitted signal based on the computation of the likelihood function of received signals under different hypotheses (modulation formats). An important class of likelihood-based algorithms for modulation classification problems first treats the unknown channels as deterministic, and replaces the channels by their estimates. In this paper, a novel theoretical bound on the performance of this class of algorithms is proposed for multiple-input multiple-output (MIMO) systems over unknown, flat fading channels. The performance bound is developed from the Cramer-Rao bound (CRB) of blind channel estimation. It provides a useful benchmark against which it is possible to compare the performance of modulation classification algorithms, and is tighter than the theoretical bound derived based on perfect channel knowledge.