We investigate the problem of antenna selection (AS) in full-duplex (FD) cooperative non-orthogonal multiple access (NOMA) systems, where a multi-antenna FD relay assists transmission from a multi-antenna base station (BS) to a far user, while at the same, the BS transmits to a near user. Specifically, based on the end-to-end signal-to-interference-plus-noise ratio at the near and far users, two AS schemes to select a single transmit antenna at both the BS and the relay, respectively, as well as a single receive antenna at relay are proposed. In order to study the ergodic sum rate and outage probability of these AS schemes, we have derived closed-form expressions assuming Rayleigh fading channels. The sum rate and outage probability of the AS schemes are also compared with the optimum selection scheme that maximizes the performance as well as with a random AS scheme. Our results show that the proposed AS schemes can deliver a near-optimal performance for near and far users, respectively.