The problem of modulation classification for a multiple-antenna (MIMO) system employing orthogonal frequency division multiplexing (OFDM) is investigated under the assumptions of unknown frequency-selective fading channels and signal-to-noise ratio (SNR). The classification problem is formulated as a Bayesian inference task and a solution is proposed based on a selection of the prior distributions that adopts a latent Dirichlet model for the modulation type and on the Bayesian network formalism. The proposed Gibbs sampling method converges to the optimal Bayesian solution and the speed of convergence is shown to improve via annealing and random restarts. While most of the existing modulation classification techniques works under the assumptions that the channels are flat fading and that a large amount of observed data symbols is available, the proposed approach performs well under more general conditions. Finally, the proposed Bayesian method is demonstrated to improve over existing non-Bayesian approaches based on independent component analysis.