The Gallager's random coding error exponent for space-time block codes (STBC) over multiple-input multiple-output (MIMO) block-fading channels, with Gaussian input distribution, is investigated. Gallager's error exponent can be used to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We first provide new, analytical expressions for Gallager's exponent of STBC systems over η-μ fading channels. The Shannon capacity and cutoff rate, which can be directly derived from Gallager's exponent, are further examined. In order to get additional insights, a high signal-to-noise ratio analysis is pursued to investigate the effects of coherence time and codeword length on the error probability. For the sake of completeness, we provide the link to previous known results on Rayleigh and Nakagami-m fading channels.