The white book released by the International Telecommunications Union (ITU) calls for extremely high-security and low-latency communication over fading channels. Under the low-latency requirement, the corresponding fading model is quasi-static fading while high-security can be achieved via covert communication. In response to the call of ITU, we study the finite blocklength performance of optimal codes for covert communication over quasi-static multi-antenna fading channels, under the covertness metric of Kullback-Leibler (KL) divergence. In particular, we study all four cases regarding the availability of channel state information (CSI) for legitimate transmitter and receiver, and assume that the warden knows perfect CSI for the channel from the legitimate transmitter to itself. Specifically, we show that, when the blocklength is $n$, the first-order covert rate satisfies the square root law, scaling as $Θ(n^{-\frac{1}{2}})$ with the coefficient determined by the traces of the channel matrices of the legitimate users and the warden, and the second-order rate vanishes. In contrast to the non-covert result of Yang et al. (TIT, 2014), we show that CSI availability at the legitimate users does not affect the finite blocklength performance for covert communication. Furthermore, we reveal the significant spatial diversity gain provided by multiple-antenna systems for covert communication. For the covertness analysis, we extend the quasi-$η$-neighborhood framework to fading channels and address challenges arising from the random channel matrices. For the reliability analysis, due to the vanishing power imposed by the covertness constraint, we refine the non-covert analysis by Yang et al. (TIT, 2014), by carefully controlling higher-order terms and exploiting the properties of covert outage probability.