The performance of physical-layer security of the classic Wyner's wiretap model over Fisher-Snedecor F composite fading channels is considered in this work. Specifically, the main channel (i.e., between the source and the legitimate destination) and the eavesdropper's channel (i.e., between the source and the illegitimate destination) are assumed to experience independent quasi-static Fisher-Snedecor F fading conditions, which have been shown to be encountered in realistic wireless transmission scenarios in conventional and emerging communication systems. In this context, exact closed-form expressions for the average secrecy capacity (ASC) and the probability of non-zero secrecy capacity (PNSC) are derived. Additionally, an asymptotic analytical expression for the ASC is also presented. The impact of shadowing and multipath fading on the secrecy performance is investigated. Our results show that increasing the fading parameter of the main channel and or the shadowing parameter of the eavesdropper's channel improves the secrecy performance. The analytical results are compared with Monte-Carlo simulations to validate the analysis.