Recently, non-orthogonal multiple access (NOMA)-based space–air–ground integrated networks (SAGINs) have gained increasing attention due to their robust communication, broader coverage, and resource-saving advantages. However, it is imperative to consider physical layer security as a crucial performance metric in NOMA-based SAGINs. This study addresses this concern by constructing a NOMA-based free space optical (FSO)/radio frequency (RF) dual-hop SAGIN system with eavesdroppers on both links. The two new fading channel models were proposed, considering the FSO link’s fog absorption and the RF link’s stochastic distribution based on Málaga and shadowed Rician distributions. The closed-form expressions for the secrecy outage probability are derived for the SAGIN system. Monte Carlo simulations were conducted to validate the theoretical findings. The results revealed the influence of fog absorption and the stochastic geometry distribution on the SAGIN system.