This paper deals with multiple-input multiple-output (MIMO) broadband wireless communication systems, employing orthogonal frequency-division multiplexing (OFDM) with cyclic prefix (CP) in combination with space-time-frequency block coding (STFBC). In order to exploit the benefits of OFDM and STFBC in highly frequency-selective channels, without incurring in a significant increase of receiver complexity, a channel shortening prefilter is inserted at the receiver, aimed at reducing the length of the MIMO channel impulse response before CP removal. Two MIMO channel shorteners are proposed, both relying on linearly-constrained minimization of the mean-output-energy of the signal at the output of the channel shortener, where the linear constraints are optimally chosen so as to maximize the signal-to-noise ratio either at the output of the channel shortener or at the input of the STFBC maximum-likelihood decoder. Unlike other solutions proposed in the literature, these shortening designs are blind ones, i.e., a priori knowledge of the MIMO channel impulse response to be shortened is not required, and can be carried out in closed-form, i.e., iterative computation of the prefilter weights is not necessary. Numerical simulations show that, without a substantial increase in computational complexity, receivers equipped with the proposed blind channel shorteners pay only a negligible performance penalty with respect to non-blind channel shorteners, while being significantly more robust to finite sample-size effects.