This paper studies antenna selection for space-time coded orthogonal frequency division multiplexing (OFDM) systems that employ multiple transmit and receive antennas. We assume that the channel state information (CSI) is exactly known at the receiver, and hence the selection is available only at the receiver. The selection criterion is based on the instantaneous signal-to-noise ratio at each receive antenna averaged over all carrier frequencies. We also assume that space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). Closed form expressions for the PEP bounds are derived for special eases. We also present numerical examples and simulation results that validate our analysis. It turns out that it is difficult to make remarks about the diversity order since the expressions are not simple, however, for some special cases with M = 2, N = 2 antennas, we show that using antenna selection, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity.