In this paper, we propose and evaluate the performance of fountain codes (FCs) based secure transmission protocols in multiple-input-multiple-output (MIMO) wireless systems, in presence of a passive eavesdropper. In the proposed protocols, a source selects its best antenna to transmit fountain encoded packets to a destination that employs selection combining (SC) or maximal ratio combing (MRC) to enhance reliability of the decoding. The transmission is terminated when the destination has a required number of the encoded packets to reconstruct the original data of the source. Similarly, the eavesdropper also has the ability to recover the source data if it can intercept a sufficient number of the encoded packets. To reduce the number of time slots used, the source can employ non-orthogonal multiple access (NOMA) to send two encoded packets to the destination at each time slot. For performance analysis, exact formulas of average number of time slots (TS) and intercept probability (IP) over Rayleigh fading channel are derived and then verified by Monte-Carlo simulations. The results presented that the protocol using NOMA not only reduces TS but also obtains lower IP at medium and high transmit signal-to-noise ratios (SNRs), as compared with the corresponding protocol without using NOMA.